
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 points $P_{1}(x_{1},y_{1})$ and $P_{2}(x_{2},y_{2})$ are on lines $l_{1}: x-y-5=0$ and $l_{2}: x-y-15=0$ respectively, determine the minimum distance from the midpoint $P$ of $P_{1}P_{2}$ to the origin.

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