
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
Sasha marked several cells of an $8 \times 13$ table such that in any $2 \times 2$ square there was an odd number of marked cells. Then he marked several more cells so that in each $2 \times 2$ square there was an even number of marked cells. What is the smallest possible total number of cells that Sasha could have marked?

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