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

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