
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
A teacher is filling in the cells of a class journal sized $7 \times 8$ (7 rows, 8 columns). In each cell, she puts one of three grades: 3, 4, or 5. After filling the entire journal, it turned out that in each row, the number of 3s is not less than the number of 4s and not less than the number of 5s. Also, in each column, the number of 4s is not less than the number of 5s and not less than the number of 3s. How many 5s could the teacher have put in?

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