
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  $\vartriangle ABC, PQ // BC$  where  $P$  and  $Q$  are points on  $AB$  and  $AC$  respectively. The lines  $PC$  and  $QB$  intersect at  $G$ . It is also given  $EF//BC$ , where  $G \in  EF, E \in AB$  and  $F\in AC$  with  $PQ = a$  and  $EF = b$ . Find value of  $BC$ .



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