
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
In the Kingdom of Bees, a special honeycomb was constructed to welcome the 2010 Spring Festival. Each hexagonal cell in the honeycomb contains a number made from condensed honey, either 0, 1, or 2. When the Spring Festival comes, bees will dance on the honeycomb in steps, with each beat of the dance passing through four numbers: 2010 (starting from a 2 and returning to 2 after exactly four steps, as shown by the arrows in the diagram). The bees can only move to an adjacent hexagonal cell sharing a common edge at each step. The total number of distinct ways for the bees to traverse four hexagonal cells in the sequence 2010 is $\qquad$.

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