
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 $f(x) = \frac{1}{3}x^3 - x^2 + m$, its maximum value on the interval $[-1, 1]$ is $\frac{2}{3}$.
1. Find the value of the real number $m$.
2. Determine the range of the function $f(x)$ on the interval $[-2, 2]$.

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