
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 rectangle $ABCD$, $AB=8$ and $BC=2$. Points $E$ and $F$ are on side $BC$ such that $BE=EF=FC$. Segments $\overline{AE}$ and $\overline{AF}$ intersect $\overline{BD}$ at points $P$ and $Q$, respectively. Find the ratio $BP:PQ:QD$ and sum these ratio components.
A) 2
B) 3
C) 4
D) 6

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