
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
Let the function be $$f(x)= \sqrt{3}\sin{x}\cos{x} + \cos^{2}x + a$$.
(1) Determine the smallest positive period of function $f(x)$ and the intervals where $f(x)$ is monotonically decreasing;
(2) When $$x \in \left[-\frac{\pi}{6}, \frac{\pi}{3}\right]$$, the sum of the maximum and minimum values of the function $f(x)$ is $$\frac{3}{2}$$. Find the value of $a$.

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