
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 $f(x) = (\cos x + \sin x)^2 + \sqrt{3}\cos 2x - 1$.

(1) Find the smallest positive period of $f(x)$ and the equation of the axis of symmetry of the graph;

(2) Find the interval of monotonic decrease for $f(x)$;

(3) Find the maximum and minimum values of $f(x)$ in the interval $\left[0, \frac{\pi}{2}\right]$.

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