
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
(1) Let $f(x) = ax + b$, and $\int_{-1}^{1} [f(x)]^2 dx = 2$, find the range of values for $f(a)$.  
(2) Find the equation of the tangent line to the function $f(x) = x^3 - 3x$ at point $P(1, -2)$.

Present the answer in LaTex format: \boxed{Your answer}
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