
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 \( f(x) = 2 \sin(x + \frac{3\pi}{4}) \cos x \), where \( x \in \mathbb{R} \).

(1) Find the minimum positive period of the function \( f(x) \);

(2) When \( x \in [-\frac{5\pi}{4}, \frac{5\pi}{4}] \), find the maximum and minimum values of the function \( f(x) \).

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