
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
Euler's formula states that for a convex polyhedron with  $V$  vertices,  $E$  edges, and  $F$  faces,  $V - E + F = 2$ .  A particular convex polyhedron has 32 faces, each of which is either a triangle or a pentagon.  At each of its  $V$  vertices,  $T$  triangular faces and  $P$  pentagonal faces meet.  What is the value of  $100P + 10T + V$ ?

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