
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
If  $f$  is a monic cubic polynomial with  $f(0)=-64$ , and all roots of  $f$  are non-negative real numbers, what is the largest possible value of  $f(-1)$ ? (A polynomial is monic if it has a leading coefficient of  $1$ .)

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