
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, \(70\) edges, and \(40\) faces, of which \(30\) are triangular and \(10\) are pentagonal. Compute the number of space diagonals in polyhedron \(Q\).

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