
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 $f(x)=\sin (2x+\frac{\pi }{6})$,

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

$\quad\qquad\qquad$ (2) Find the range of the function $f(x)$ on the interval $-\frac{\pi }{12}\leq x\leq \frac{\pi }{2}$.

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