
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 $f(x)=3\sin(2x+ \frac {\pi}{4})$, where $x\in\mathbb{R}$:
1. Determine the intervals of monotonicity for $f(x)$.
2. Find the set of values of the independent variable $x$ for which $f(x)$ attains its maximum and minimum values, and state what those maximum and minimum values are.

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