
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 that \( f(x) \) is an odd function defined on \( \mathbf{R} \), and the function \( y = f(x+1) \) is an even function. When \( -1 \leq x \leq 0 \), \( f(x) = x^3 \). Find \( f\left( \frac{9}{2} \right) \).

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