
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
If moving points $A(x_{1}, y_{1})$ and $B(x_{2}, y_{2})$ are on the lines $l_{1}$: $x+y-7=0$ and $l_{2}$: $x+y-5=0$ respectively, calculate the minimum distance from the midpoint $M$ of $AB$ to the origin.

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