
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 that $x_{1}, x_{2}$ are two adjacent zeros of the function $f(x) = 4\cos{\omega x}\sin(\omega x + \frac{\pi}{6}) + 1$, and it satisfies $|x_{1} - x_{2}| = \pi$, where $\omega > 0$.

(Ⅰ) Find the value of $\omega$;

(Ⅱ) Find the maximum and minimum values of $f(x)$ in the interval $\left[-\frac{\pi}{6}, \frac{\pi}{4}\right]$.

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