
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 slanted line extending from $(c,0)$ to $(4,4)$ divides the entire region into two regions of equal area, where six unit squares are arranged in the coordinate plane with the lower left corner at the origin. Find the value of $c$.

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