
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 \( f(x) = x^3 - ax^2 + (a^2 - 2)x + 1 \), if there exists \( m > 0 \) such that \( f(m) \leq 0 \), what is the maximum value of the real number \( a \)?

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