
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
One of the simplest multicellular organisms, the algae Volvox, is a spherical shell composed mainly of heptagonal, hexagonal, and pentagonal cells (i.e., cells having seven, six, or five neighboring cells; three cells meet at each "vertex"). There are some specimens that have quadrilateral and octagonal cells as well, but biologists have noticed that if there are no such "non-standard" cells (with fewer than five and more than seven sides), then there are always 12 more pentagonal cells than heptagonal cells. Can you explain this fact?

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