
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
A  $\emph{planar}$  graph is a connected graph that can be drawn on a sphere without edge crossings. Such a drawing will divide the sphere into a number of faces. Let  $G$  be a planar graph with  $11$  vertices of degree  $2$ ,  $5$  vertices of degree  $3$ , and  $1$  vertex of degree  $7$ . Find the number of faces into which  $G$  divides the sphere.

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