
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 $f\left( x \right)=\left( 1-2\cos^{2}x \right)\sin \left( \frac{3\pi}{2}+\theta \right)-2\sin x\cos x\cos \left( \frac{\pi}{2}-\theta \right)$ $\left( \left| \theta \right|\leqslant \frac{\pi}{2} \right)$ is monotonically increasing on $\left[ -\frac{3\pi}{8},-\frac{\pi}{6} \right]$ and $f\left( \frac{\pi}{8} \right)\leqslant m$, determine the range of the real number $m$.

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