
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
An engineer plans to construct a pavilion with eight vertical columns located at the vertices of a regular octagon lying horizontally on the ground. The columns support a non-horizontal reflective surface. The heights of the columns at vertices $A$, $B$, $C$, and $D$ are $15$, $12$, $14$, and $13$ meters respectively. What is the height, in meters, of the column at vertex $G$, directly opposite to column $C$?
A) 15
B) 14.5
C) 15.5
D) 16
E) 16.5

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