
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 r be the number of pairs of $1 socks, s be the number of pairs of $2 socks, and t be the number of pairs of $4 socks. If r+s+t=10, 1r+2s+4t=30, and r, s, t are integers ≥ 1, find the value of r.

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