
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 length of the chord intercepted by the line $x+2y-5+\sqrt{5}=0$ on the circle $x^{2}+y^{2}-2x-4y=0$ is given by the length of the line segment connecting the two intersection points of the line and the circle.

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