
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 an ellipse $\dfrac {x^{2}}{4}+ \dfrac {y^{2}}{m}=1(m > 0)$, whose focal chord $F\_1F\_2$ is the diameter of a circle that intersects with the ellipse in the first quadrant at point $P$. If the area of $\triangle PF\_1F\_2$ is $1$, then the value of $m$ is _____.

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