
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 convex polyhedron has 40 faces, consisting of triangles and hexagons only. At each vertex, $T$ triangular faces and $H$ hexagonal faces meet such that each vertex adheres to the property $2T+H=7$. Determine the value of $100H+10T+V$.

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