
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
Find the smallest positive integer  $ K$  such that every  $ K$ -element subset of  $ \{1,2,...,50 \}$  contains two distinct elements  $ a,b$  such that  $ a\plus{}b$  divides  $ ab$ .

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