
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 $f(x)=2\sin x\cos x+a\cos x-2x$, the slope of the tangent line to the curve $y=f(x)$ at the point $\left( \frac {\pi}{6},f\left( \frac {\pi}{6}\right)\right)$ is $-2$.  
$(1)$ Find the value of the real number $a$;  
$(2)$ When $x\in\left[- \frac {\pi}{6}, \frac {7\pi}{6}\right]$, find the maximum value of the function $f(x)$.

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