
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
In the Cartesian coordinate plane $(xOy)$, line $l$ is translated by 3 units in the positive direction of the $x$-axis and by 5 units in the positive direction of the $y$-axis to obtain line $l_{1}$. Then, line $l_{1}$ is translated by 1 unit in the positive direction of the $x$-axis and by 2 units in the negative direction of the $y$-axis, and it coincides with line $l$. If line $l$ and line $l_{1}$ are symmetric about the point $(2,3)$, find the equation of line $l$.

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