
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
We have placed a 1 forint coin heads up in every cell of a $3 \times 3$ grid. What is the minimum number of coins that need to be flipped so that there are no three heads or three tails in any row, column, or diagonal?

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