
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
Let \( f(x) = 3x - ax^3 \) and \( g(x) = b + 3x + cx^2 + dx^3 \), where \( a, b, c, d \in \mathbb{R} \).

1. Find the value of \( a \) such that, for \( x \in [-1, 1] \),
   \[
   |f(x)| \leq 1;
   \]

2. Find the values of \( b, c, \) and \( d \) such that, for \( x \in [-1, 1] \), 
   \[
   |g(x)| \leq 1.
   \]


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