
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
There are four locks and six keys. It is known that each key opens exactly 2 locks. Moreover, no two keys open exactly the same pairs of locks. Determine, in no more than 13 tests, which key opens which two locks. In one test, you can insert a key into a lock and check if it opens it or not.

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