
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
If the function $f(x) = \sqrt{3}\sin{2x} + 2\cos^2{x} + m$ has a minimum value of 3 on the interval $[0, \frac{\pi}{2}]$, find the value of the constant $m$ and the maximum value of this function when $x \in [a, a+\pi]$ (where $a$ can be any real number).

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