
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 \( f(x)=\sin \left(x+\frac{\pi}{6}\right)+\sin \left(x-\frac{\pi}{6}\right)+a \cos x+b \) (where \(a\) and \(b\) are real constants),

1. Find the smallest positive period of the function \( f(x) \).
2. If \( f(x) \) is monotonically increasing on the interval \(\left[-\frac{\pi}{3}, 0\right]\) and attains its minimum value of 2, determine the values of \(a\) and \(b\).

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