
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 the triangle \(ABC\), \(AB = AC = 1\), \(D\) and \(E\) are the midpoints of \(AB\) and \(AC\) respectively. Let \(P\) be a point on \(DE\) and let the extensions of \(BP\) and \(CP\) meet the sides \(AC\) and \(AB\) at \(G\) and \(F\) respectively. Find the value of \(\frac{1}{BF} + \frac{1}{CG}\).

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