
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 $f(x) = x^3 + ax^2 - a^2x + m$ ($a > 0$).
1. If $a=1$, and the function $f(x)$ has three distinct zeros, find the range of the real number $m$.
2. If for any $a \in [3, 6]$, the inequality $f(x) \leq 1$ always holds on $[-2, 2]$, find the range of the real number $m$.

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