
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 $f(x) = 2\sin x \cdot \cos \left( x + \frac{\pi}{3} \right)$.

(Ⅰ) Find the intervals of monotonicity for the function $f(x)$;

(Ⅱ) Find the maximum and minimum values of the function $f(x)$ in the interval $\left[ 0, \frac{\pi}{2} \right]$ and the values of $x$ at which these extrema are attained.

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