
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 point $P$ is randomly chosen on a line segment $AB$ of length $10$cm. A square is constructed with side length equal to the length of segment $AP$. The probability that the area of this square is between $25\text{cm}^2$ and $49\text{cm}^2$ is ____.

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