
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 a regular tetrahedron $\mathrm{ABCD}$ with a point $\mathrm{P}$ inside it such that $P A=P B=\sqrt{11}$ and $P C=P D=\sqrt{17}$. What is the side length of the tetrahedron $\mathrm{ABCD}$?

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