
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
The Evil League of Evil is plotting to poison the city's water supply. They plan to set out from their headquarters at  $(5, 1)$  and put poison in two pipes, one along the line  $y=x$  and one along the line  $x=7$ . However, they need to get the job done quickly before Captain Hammer catches them. What's the shortest distance they can travel to visit both pipes and then return to their headquarters?

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