
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. Given a point A $(a,6)$ and the distance $d=4$ from the point to the line $3x-4y=2$, find the value of $a$.
2. Find a point $P$ on the line $x+3y=0$ such that its distance from the origin is equal to its distance from the line $x+3y-2=0$.

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