
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 $f(x) = 2\sin\left(x + \frac{\pi}{6}\right) - 2\cos x$.
(Ⅰ) Find the interval where the function $f(x)$ is monotonically increasing;
(Ⅱ) If $f(x) = \frac{6}{5}$, find the value of $\cos\left(2x - \frac{\pi}{3}\right)$.

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