
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 that a line extends from $(c, 0)$ to $(2, 2)$ and divides a region into two regions of equal area in a coordinate plane, where four unit squares form a larger square with a side length of 2 units with the lower left corner at the origin, determine the value of $c$.

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