
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 that point A lies on the line $x-y=0$, and point B lies on the line $x+y=0$. The line segment AB passes through the point $(-1,0)$, and its midpoint lies on the ray $x-2y=0$ where $x≤0$. Find the length of the line segment AB.

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