
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. If the projection of the origin onto line $l$ is $(2, -1)$, find the equation of line $l$.
2. In $\triangle ABC$, with point $A(4, -1)$, the midpoint of $AB$ is $M(3, 2)$, and the centroid is $P(4, 2)$. Find the length of side $BC$.

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