
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 triangle with vertices $A=(2,2)$, $B=(6,2)$, and $C=(5,5)$ plotted on an $8\times6$ grid, and a smaller rectangle within the grid defined by its diagonal with endpoints $(1,1)$ and $(6,5)$. Determine the fraction of the grid area covered by the portion of the triangle that lies within the smaller rectangle.

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