
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 that the line $l_{1}$: $x-my+1=0$ passes through the fixed point $A$, and the line $l_{2}$: $mx+y-m+3=0$ passes through the fixed point $B$. The lines $l_{1}$ and $l_{2}$ intersect at point $P$. Find $|PA|^{2}+|PB|^{2}$.

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