
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
The function \( F(x) = i \cos^{2} x + 2 \sin x \cos x - \sin^{2} x + A x + B \) on the interval \(\left[0, \frac{3}{2} \pi \right]\) has maximum value \( M(A, B) \). Find the minimum value of \( M(A, B) \) when the real numbers \( A \) and \( B \) vary.

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