
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
Screws are sold in packs of  $10$  and  $12$ . Harry and Sam independently go to the hardware store, and by coincidence each of them buys exactly  $k$  screws. However, the number of packs of screws Harry buys is different than the number of packs Sam buys. What is the smallest possible value of  $k$ ?

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