
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 vectors $\overrightarrow{a}=(2\cos x,1)$ and $\overrightarrow{b}=(\cos x, \sqrt {3}\sin 2x+m)$, and a function $f(x)= \overrightarrow{a} \cdot \overrightarrow{b}-1$.
(1) Find the interval(s) where $f(x)$ is increasing on $x\in[0,\pi]$.
(2) When $x\in[0, \frac {\pi}{6}]$, the inequality $-4\leqslant f(x)\leqslant 4$ always holds. Find the range of the real number $m$.

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