
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 grid consists of 16 equally spaced points (4x4 grid), where each point is 2 units away from its nearest neighbors, both horizontally and vertically. Calculate the area, in square units, of the region where the following two triangles overlap:
1. Triangle formed by connecting points at (0,0), (6,2), and (2,6).
2. Triangle formed by connecting points at (6,6), (0,2), and (2,0).

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