
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 $f(x) = 2\sin(3x + \frac{\pi}{4})$:
(Ⅰ) Find the smallest positive period of function $f(x)$.
(Ⅱ) Find the intervals where function $f(x)$ is monotonically increasing.
(Ⅲ) When $x \in \left[-\frac{\pi}{6}, \frac{\pi}{6}\right]$, determine the maximum and minimum values of the function.

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