
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
There are numbers $1, 2, \cdots, 36$ to be filled into a $6 \times 6$ grid, with each cell containing one number. Each row must be in increasing order from left to right. What is the minimum sum of the six numbers in the third column?

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