
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 $f(x) = 2\sin(2x + \frac{\pi}{4})$, where $x \in \mathbb{R}$,  
(1) Determine the smallest positive period of function $f(x)$, the equation of the axis of symmetry, and the monotonic intervals;  
(2) Find the maximum and minimum values of function $f(x)$ on the interval $\left[0, \frac{\pi}{2}\right]$, and the values of $x$ at which these extreme values are attained.

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