
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
A convex polyhedron $Q$ has $30$ vertices, $72$ edges, and $44$ faces, of which $32$ are triangular and $12$ are quadrilaterals. Determine the number of space diagonals inside $Q$.

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