
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
Several gnomes, having loaded their luggage onto ponies, set out on a long journey. They were spotted by trolls, who counted 36 legs and 15 heads in the caravan. How many gnomes were there, and how many ponies?

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