
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 $f(x) = -x^2 + 2x + a$ (where $0 \leq x \leq 3$, $a \neq 0$), let the maximum value of the function be $m$ and the minimum value be $n$. Find the values of $m$ and $n$ in terms of $a$.

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