
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
Darwin takes an  $11\times 11$  grid of lattice points and connects every pair of points that are 1 unit apart, creating a  $10\times 10$  grid of unit squares. If he never retraced any segment, what is the total length of all segments that he drew?

*Ray Li.*

<details><summary>Clarifications</summary>[list=1][*]The problem asks for the total length of all *unit* segments (with two lattice points in the grid as endpoints) he drew.[/list]</details>

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