
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
For the function $f(x) = 2\sin\left(\frac{1}{2}x - \frac{\pi}{6}\right)$, where $x \in \mathbb{R}$:
(1) Determine its amplitude, period, and initial phase;
(2) Calculate the value of $f\left(\frac{4\pi}{3}\right)$;
(3) Find the maximum and minimum values of the function, as well as the values of $x$ at which these extrema occur;
(4) Determine the intervals where the function is increasing.

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