
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 $\overrightarrow {a}=( \sqrt {3}\sin x, m+\cos x)$ and $\overrightarrow {b}=(\cos x, -m+\cos x)$, and a function $f(x)= \overrightarrow {a}\cdot \overrightarrow {b}$
(1) Find the analytical expression of function $f(x)$;
(2) When $x\in[- \frac {\pi}{6}, \frac {\pi}{3}]$, the minimum value of $f(x)$ is $-4$. Find the maximum value of the function $f(x)$ and the corresponding $x$ value.

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