
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 $6 \times 6$ chessboard, there is a dwarf on each square. The dwarves can only move to an orthogonally adjacent square. Which dwarves can reach the bottom right corner such that they pass through each of the 36 squares exactly once along the way?

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