
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 certain convex polyhedron has 30 faces, each of which is either a triangle or a hexagon. 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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