
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 \( f(x)=4 \cos x \cdot \sin \left(x+\frac{7 \pi}{6}\right)+a \) has a maximum value of 2.
(1) Find the value of \( a \) and the smallest positive period of \( f(x) \).
(2) Find the interval where \( f(x) \) is monotonically decreasing.

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