
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 $\sin \left( \frac {\pi}{3}+ \frac {\alpha}{6}\right)=- \frac {3}{5}$ and $\cos \left( \frac {\pi}{12}- \frac {\beta}{2}\right)=- \frac {12}{13}$, with $-5\pi < \alpha < -2\pi$ and $- \frac {11\pi}{6} < \beta < \frac {\pi}{6}$, find the value of $\sin \left( \frac {\alpha}{6}+ \frac {\beta}{2}\right)$.

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