
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
(1) It is known that line $l$ passes through point $P(4,1)$, and the intercepts on the two coordinate axes are equal. Find the equation of line $l$;  
(2) It is known that line $l$ passes through point $P(3,4)$, and the slope angle of line $l$ is $\theta$ ($\theta \neq 90°$). If line $l$ also passes through another point $(\cos\theta, \sin\theta)$, find the equation of line $l$ at this time.

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