
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 24 faces, each of which is either a hexagon or a triangle. At each of its \(V\) vertices, \(T\) triangular faces and \(H\) hexagonal faces meet. What is the value of \(100H+10T+V\)?

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