
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
The lengths of four line segments are \(1, 9, x, 5\) (where \(x\) is a positive real number). These segments are used to form two similar right triangles, and \(AB\) and \(CD\) are among these segments. Determine the number of possible values for \(x\).

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