step-by-step

name	step-by-step
description	Decompose mathematical problems into sub-expressions, evaluate each one with the calculator tool, and present the full working chain. Handles arithmetic, trigonometry, logarithms, and financial formulas.

Step-by-step computation skill.

When to activate

Use this skill when the user asks you to:

• Solve a math problem or evaluate an expression
• Show your working or explain how to compute something
• Calculate financial values (interest, payments, returns)
• Convert units or work with formulas
• Verify a number or check a calculation

Methodology

1. Parse the problem

Use the think tool to identify:

• What quantity the user wants computed
• Which formula or approach applies
• What the input values are (with units)
• Whether any values need conversion first

2. Decompose into steps

Break the problem into calculator-sized sub-expressions. Each step should evaluate to a single number. Plan the sequence so each step builds on the previous result.

Example decomposition for compound interest A = P(1 + r/n)^(nt):

1. Calculate the periodic rate: r / n
2. Add 1: 1 + <step1>
3. Calculate the exponent: n * t
4. Raise to power: <step2> ** <step3>
5. Multiply by principal: P * <step4>

3. Evaluate each step

Call the calculator for every sub-expression. Present each step as:

Step N: <description>
  <expression> = <result>

Never skip steps or do mental arithmetic. The calculator is exact and its results are auditable.

4. Handle calculator limitations

The calculator supports:

• Arithmetic: +, -, *, /, //, %, **
• Functions: sin, cos, tan, asin, acos, atan, sqrt, log, log10, log2, exp, abs, ceil, floor, round, pow
• Constants: pi, e, tau, inf

It does NOT support:

• Variable assignment (x = 5)
• Summation, product, or loop notation
• Symbolic algebra
• Matrix operations
• Complex numbers

For unsupported operations, use the python tool. State clearly when you are switching to python and why.

5. Verify the result

After computing the final answer, verify it using one of:

• Reverse calculation: work backwards from the answer
• Estimation: check the order of magnitude makes sense
• Alternative formula: use a different approach to get the same result

6. Present the answer

State the final answer with:

• The value, rounded appropriately for context
• Units (if applicable)
• A one-line summary of what it means in plain language

MUST

• Call the calculator for every arithmetic step, no exceptions
• Show every intermediate step and its result
• Include units throughout the working
• Verify the final answer with a check step
• Use the think tool to plan the decomposition before calculating

MUST NOT

• Present a number without having calculated it with a tool
• Skip intermediate steps even if they seem obvious
• Use the calculator for problems it cannot handle (use python instead)
• Round intermediate results -- keep full precision until the final answer
• Assume formula correctness from memory -- derive or verify first