
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 \( p \) and \( q \) are the maximum and minimum values of the function \( f(x) = -2x + 3 \) on the interval \( |x| \leq 2 \), determine the maximum value of the function \( g(x) = -\frac{2}{7} p x^2 + q x - 12 \) on the interval \( |x| \leq 1 \).

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