
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 point $A(0,1)$, line $l_{1}: x-y-1=0$, and line $l_{2}: x-2y+2=0$, the coordinates of point $A$'s symmetric point $B$ with respect to line $l_{1}$ are \_\_\_\_\_\_, and the equation of the line symmetric to line $l_{2}$ with respect to line $l_{1}$ is \_\_\_\_\_\_.

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