
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 $A-BCD$ with the radius of its circumscribed sphere $R= \dfrac { \sqrt {3}}{2}$, points $P$ and $Q$ are on $AB$ and $BC$ respectively, satisfying $\dfrac {AP}{PB}= \dfrac {CQ}{QB}=5$, and $DP\perp PQ$. Calculate the height of this regular tetrahedron.

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