
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) Find the equation of the line that passes through the point (1, 3) and has equal intercepts on both coordinate axes.  
(2) Find the locus of points that are equidistant from the lines $2x+3y-5=0$ and $4x+6y+8=0$.

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