
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 vectors $\overrightarrow {a} = (\tan(\theta+ \frac {\pi}{12}), 1)$ and $\overrightarrow {b} = (1, -2)$, and knowing that $\overrightarrow {a}$ is perpendicular to $\overrightarrow {b}$, find $\tan(2\theta+ \frac {5\pi}{12})$.

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