
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 $l$ passing through the point $(1, 4)$:
$(1)$ If line $l$ is parallel to the line $l_{1}: y = 2x$, find the equation of line $l$ and the distance between $l$ and $l_{1}$;
$(2)$ If the intercepts of line $l$ on the $x$-axis and the $y$-axis are both equal to $a$, and $a \neq 0$, find the value of $a$.

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