
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 plane rectangular coordinate system $xOy$, a line $l$ is translated $3$ units along the positive $x$-axis and $5$ units along the positive $y$-axis to obtain line $l_{1}$. Line $l_{1}$ is then translated $1$ unit along the positive $x$-axis and $2$ units along the negative $y$-axis, and coincides with line $l$ again. If line $l$ is symmetric about point $(2,3)$ with line $l_{1}$, then the equation of line $l$ is ____.

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