
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
Given a triangle \( \triangle ABC \) and an arbitrary point \( P \) inside it, construct lines \( IF \parallel BC \), \( EH \parallel AC \), and \( DG \parallel AB \). Calculate the value of \( \frac{IF}{BC} + \frac{EH}{AC} + \frac{DG}{AB} \).

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