
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
The eccentricity of the hyperbola $C$: $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1(a>0,b>0)$ is $\sqrt{3}$. When $a=1$, the line $x-y+m=0$ intersects the hyperbola $C$ at two distinct points $A$ and $B$, and the midpoint of the line segment $AB$ lies on the circle $x^{2}+y^{2}=5$. Find the value of $m$.

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