
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 $\overrightarrow{a} = (\sin x, m\cos x)$ and $\overrightarrow{b} = (3, -1)$.
(1) If $\overrightarrow{a} \parallel \overrightarrow{b}$ and $m=1$, find the value of $2\sin^2x-3\cos^2x$;
(2) If the graph of the function $f(x) = \overrightarrow{a} \cdot \overrightarrow{b}$ is symmetric about the line $x= \frac{2\pi}{3}$, find the range of the function $f(2x)$ on the interval $\left[ \frac{\pi}{8}, \frac{2\pi}{3} \right]$.

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