
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
In hexagon $ABCDEF$, two interior angles $A$ and $B$ are $90^\circ$ and $120^\circ$ respectively. Two other angles, $C$ and $D$, are equal. The fifth angle, $E$, is half of the sum of angles $C$ and $D$, and the last angle $F$ is $30^\circ$ less than twice angle $C$. Determine the measure of the largest angle.

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