
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
On a grid of equilateral triangles with side length 1, we have selected four grid points that form the vertices of a parallelogram \(\mathcal{P}\). The area of \(\mathcal{P}\) is \(\sqrt{3}\) square units. What is the sum of the lengths of the grid segments that lie inside \(\mathcal{P}\)?

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