
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 triangle \( \triangle ABC \) with side lengths \( BC = a \), \( CA = b \), and \( AB = c \), and an arbitrary point \( P \) inside the triangle, find the value of \( \frac{a'}{a} + \frac{b'}{b} + \frac{c'}{c} \), where lines parallel to the sides of the triangle are drawn through point \( P \), intersecting the sides \( BC \), \( CA \), and \( AB \) at \( DE = a' \), \( FG = b' \), and \( HI = c' \), respectively.

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