
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
Given a workshop of a textile factory with $m$ skilled workers and $n$ looms, define $a_{ij}$ to equal 1 if the $i$-th worker operated the $j$-th loom, and 0 otherwise. Calculate the meaning of the equation $a_{41}+a_{42}+a_{43}+\ldots+a_{4n}=3$.

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