
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
Aston wants to colour exactly three of the cells in the grid shown so that the coloured grid has rotational symmetry of order two. Each of the cells in the grid is a square. In how many ways can Aston do this?

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