
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 hexagon $ABCDEF$ has internal angles where $\angle A = 100^\circ$ and $\angle B = 120^\circ$. Angles $C$ and $D$ are equal, and angle $E$ is $30^\circ$ more than the average of angles $C$, $D$, and $F$. Find the measure of the largest angle in the hexagon.

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