
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 architect is building a structure consisting of vertical pillars placed at the vertices of a regular hexagon $ABCDEF$, lying horizontally on the ground. The heights of pillars at $A$, $B$, and $C$ are $8$, $11$, and $12$ meters, respectively. Find the height, in meters, of the pillar at $D$.

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