
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
Petya has a 3x3 grid. He places pieces in the cells according to the following rules:

- No more than one piece can be placed in each cell;
- A piece can be placed in an empty cell if the total number of pieces already present in the corresponding row and column is even (0 is considered an even number).

What is the maximum number of pieces Petya can place?

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