
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 line passes through the fixed point P(2, 1).
(1) Find the equation of the line that passes through point P and has equal intercepts on both coordinate axes;
(2) If the line $l$ passing through point P intersects the positive half of the x-axis and y-axis at points A and B respectively, find the minimum value of the area of $\triangle AOB$ and the equation of line $l$ at this condition.

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