
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
Grandma has two balls of yarn: one large and one small. From the large ball, she can either knit a sweater and three socks, or five identical hats. From the small ball, she can either knit half a sweater or two hats. (In both cases, all the yarn will be used up.) What is the maximum number of socks Grandma can knit using both balls of yarn? Justify your answer.

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