
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
Let  $Z$  shape be a shape such that it covers  $(i,j)$ ,  $(i,j+1)$ ,  $(i+1,j+1)$ ,  $(i+2,j+1)$  and  $(i+2,j+2)$  where  $(i,j)$  stands for cell in  $i$ -th row and  $j$ -th column on an arbitrary table. At least how many  $Z$  shapes is necessary to cover one  $8 \times 8$  table if every cell of a  $Z$  shape is either cell of a table or it is outside the table (two  $Z$  shapes can overlap and  $Z$  shapes can rotate)?

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