
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 $f(x) = \cos 2x + 2\sin x \cdot \sin$.  
(1) Find the smallest positive period of $f(x)$, its maximum value, and the set of $x$ values for which it attains its maximum value;  
(2) If $A$ is an acute angle of the triangle $\triangle ABC$ and $f(A) = 0$, with $b = 5$ and $a = 7$, find the area of $\triangle ABC$.

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