
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 that the vertex of angle $α$ is at the origin of the coordinate system, its initial side coincides with the non-negative semi-axis of the $x$-axis, and its terminal side passes through point $P(-3, \sqrt {3})$.
(1) Find the value of $\sin 2α-\tan α$;
(2) If the function $f(x)=\cos (x-α)\cos α-\sin (x-α)\sin α$, find the range of the function $g(x)- \sqrt {3}f( \frac {π}{2}-2x)-2f^{2}(x)$ in the interval $[0, \frac {2π}{3}]$.

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