
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
ABC is an acute-angled triangle. B' is a point on the perpendicular bisector of AC on the opposite side of AC to B such that angle AB'C = 2∠A. A' and C' are defined similarly (with ∠CA'B = 2∠C, ∠BC'A = 2∠B). The lines AA' and B'C' meet at A". The points B" and C" are defined similarly. Find AA'/A"A' + BB'/B"B' + CC'/C"C'.

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