
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 the Cartesian coordinate system, the vertices of $\triangle ABC$ are $A(-1, 0)$, $B(3, 0)$, and $C(0, 2)$. It is known that a moving line $y = m (0 < m < 2)$ intersects segments $AC$ and $BC$ at points $D$ and $E$ respectively, and there exists a point $P$ on the x-axis such that $\triangle DEP$ is an isosceles right triangle. Find the value of $m$.

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