
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
(The full score of this question is 12 points)  
The function $y = A\sin(\omega x + \phi)$ ($A > 0$, $\omega > 0$, $0 \leq \phi \leq 2\pi$) takes only one maximum value and one minimum value within $x \in (0, 7\pi)$, and when $x = \pi$, $y_{\text{max}} = 3$; when $x = 6\pi$, $y_{\text{min}} = -3$. (1) Find the analytical expression of this function; (2) Find the intervals of monotonic increase for this function.

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