
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 system xOy, line $l$ is translated 3 units in the positive direction of the x-axis and 5 units in the positive direction of the y-axis to obtain line $l_1$. Then, line $l_1$ is translated 1 unit in the positive direction of the x-axis and 2 units in the negative direction of the y-axis, and it coincides with line $l$ again. The distance between line $l$ and line $l_1$ is \_\_\_\_\_\_.

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