
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
Triangle $ABC$ has side $AB = 10$ inches. A line $DEF$ is drawn parallel to line $AB$, where point $D$ is on segment $AC$ and point $E$ is on segment $BC$. Line $AE$ extended bisects angle $FEC$. Line $DEF$ has length $4$ inches. Parallelogram $PQRS$ is such that $PQ$ is parallel to and equal in length to $AB$, and vertex $Q$ lies on $BC$ and vertex $P$ on $AC$. Calculate $CE$, the length of segment $CE$ in inches.
A) $\frac{18}{3}$
B) $\frac{20}{3}$
C) $\frac{22}{3}$
D) $\frac{24}{3}$
E) $\frac{26}{3}$

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