
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
Given a circle defined by the equation $(x-m)^{2}+y^{2}= \frac{137}{144}$, find the range of the real number $m$ such that the point $(P_{1},P_{2})$ lies inside the circle, where $P_{1}$ and $P_{2}$ are the probabilities of obtaining two non-coincident lines and intersecting lines respectively when throwing a dice twice.

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