
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 function $f(x) = A\sin(\omega x + \frac{\pi}{6})$ ($A>0$, $\omega>0$) has a maximum value of 2, and its smallest positive period is $2\pi$.
(Ⅰ) Find the analytical expression of the function $f(x)$;
(Ⅱ) If $g(x) = \cos(x) \cdot f(x)$, find the maximum and minimum values of $g(x)$ in the interval $\left[-\frac{\pi}{6}, \frac{\pi}{4}\right]$.

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