
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 that the sequence $\{a_n\}$ is a geometric sequence, and the sequence $\{b_n\}$ is an arithmetic sequence. If $a_1-a_6-a_{11}=-3\sqrt{3}$ and $b_1+b_6+b_{11}=7\pi$, then the value of $\tan \frac{b_3+b_9}{1-a_4-a_3}$ is ______.

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