
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 $$f(x)=A\sin(wx+\varphi) \quad (A>0, w>0, |\varphi|<\frac{\pi}{2})$$, the coordinates of one of its highest points are $$(\frac{\pi}{6}, 2)$$, and the coordinates of one of its adjacent lowest points are $$(\frac{2\pi}{3}, -2)$$.

(1) Find the analytical expression of the function $f(x)$;  
(2) Find the intervals of monotonic increase of the function $f(x)$ and the equation of its axis of symmetry.

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