
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
Given the function $f(x) = ax^3 + cx + d$ ($a \neq 0$) is an odd function over $\mathbb{R}$, and when $x=1$, $f(x)$ reaches an extreme value of $-2$.
1. Find the expression for function $f(x)$.
2. Determine the intervals of monotonicity and the maximum value of $f(x)$.

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