
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 $l$ passes through the intersection point $A$ of line $l_1: 2x+y-5=0$ and line $l_2: x-2y=0$,
(1) When the intercepts of line $l$ on the two coordinate axes are equal, find the equation of line $l$;
(2) When the distance from point $B(5,0)$ to line $l$ is maximized, find the equation of line $l$.

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