
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 $a=(\sin x,m\cos x)$ and $b=(3,-1)$.

(1) If $a$ is parallel to $b$, and $m=1$, find the value of $2\sin ^{2}x-3\cos ^{2}x$.

(2) If the graph of the function $f(x)=a\cdot b$ is symmetrical about the line $x= \frac{2π}{3}$, find the range of the function $f(2x)$ on the interval $[\frac{\pi}{8}, \frac{2π}{3}]$.

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