
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
On side \( AB \) of parallelogram \( ABCD \), point \( F \) is selected, and on the extension of side \( BC \) beyond vertex \( B \), point \( H \) is chosen such that \( \frac{AB}{BF} = \frac{BC}{BH} = 5 \). Point \( G \) is selected so that \( BFGH \) is a parallelogram. Line \( GD \) intersects \( AC \) at point \( X \). Find \( AX \), if \( AC = 100 \).

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