
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 \( y = f(x) \) be an odd function on \( (-\infty, +\infty) \) such that \( f(x+2) = -f(x) \). When \( -1 \leq x \leq 1 \), \( f(x) = x^3 \).

1. Find the explicit form of \( f(x) \) for \( x \in [1, 5] \).
2. If \( A = \{ x \mid f(x) > a, x \in \mathbf{R} \} \) and \( A \neq \varnothing \), determine the range of the real number \( a \).

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