
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
Bethan is playing a game on an  $n\times n$  grid consisting of  $n^2$  cells. A move consists of placing a counter in an unoccupied cell  $C$  where the  $2n-2$  other cells in the same row or column as  $C$  contain an even number of counters. After making  $M$  moves Bethan realises she cannot make any more moves. Determine the minimum value of  $M$ .

*United Kingdom, Sam Bealing*

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