
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
A real number \( x \) is chosen uniformly at random from the interval \( (0, 10) \). Compute the probability that \( \sqrt{x}, \sqrt{x+7} \), and \( \sqrt{10-x} \) are the side lengths of a non-degenerate triangle.

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