
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, a line $l: ax+y-1=0$ passing through a fixed point $P$ intersects with a line $m: x-ay+3=0$ passing through a fixed point $Q$ at point $M$. Find the value of $|MP|^{2}+|MQ|^{2}$.

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