
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 $f(x)=2\sqrt{3}\sin{x}\cos{x}+2\sin^2{x}+a$, and $f(\frac{π}{3})=3$. Find the value of $a$ and the minimum positive period of $f(x)$; If $x\in \left[0,m\right]$ and $f(x)\geqslant 0$, find the maximum value of the real number $m$.

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