
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
Sarah went to the market and bought 15 pairs of socks for a total of $45. Some socks she bought cost $2 per pair, some $4 per pair, and some $5 per pair. If she bought at least one pair of each type, determine the number of pairs of $2 socks that Sarah bought.

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