
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 the two equations of curves, $y^2 = x$ and $x + 2y = 10$, find the distance between their points of intersection.
A) $2\sqrt{65}$
B) $4\sqrt{11}$
C) $2\sqrt{55}$
D) $10$

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