
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 the function \( f(x) = x^2 - 6x + 5 \), determine the region in the plane where the points \((x, y)\) satisfy both \( f(x) + f(y) \leq 0 \) and \( f(x) - f(y) \geq 0 \). Also, plot the graph of this region.

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