
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 line passes through point P(3, 2) and satisfies the following conditions. Find the equation of the line:
(1) The angle of inclination is twice the angle of inclination of the line $x-4y+3=0$;
(2) It intersects the positive semi-axes of x and y at points A and B, respectively, and the area of $\triangle AOB$ is minimized (O is the origin).

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