
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 a regular hexagon $ABCDEF$, points $P$, $Q$, $R$, $S$, $T$, and $U$ are chosen on sides $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{DE}$, $\overline{EF}$, and $\overline{FA}$ respectively, such that each side of the hexagon is divided into three equal segments. What is the ratio of the area of hexagon $PQRSTUV$ to the area of hexagon $ABCDEF$?
A) $\frac{1}{3}$
B) $\frac{1}{9}$
C) $\frac{1}{18}$
D) $\frac{1}{27}$
E) $\frac{16}{54}$

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