
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
Henry went to the market and bought 15 pairs of socks for a total of $40. Some of the socks he bought cost $2 per pair, some cost $3 per pair, and some cost $5 per pair. If he bought at least one pair of each type, find the number of pairs of $2 socks Henry bought.

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