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

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