
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
In triangle $ABC$, $AB=2$, $AC=5$, and $\cos A= \frac {4}{5}$. A point $P$ is chosen randomly inside triangle $ABC$. The probability that the area of triangle $PAB$ is greater than $1$ and less than or equal to $2$ is __________.

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