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

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