
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
Let the number of pairs of $2 socks be $x$, the number of pairs of $3 socks be $y$, and the number of pairs of $5 socks be $z$. Given that Henry bought 15 pairs of socks, $x+y+z=15$. Also, given that the total cost is $\36, 2x+3y+5z=36$.

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