
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
A total of 315 dog sleds consisting of either pairs or triples competed in a Northern sled dog race. Sixty percent of all pairs and one-third of all triples reached the finish line within the time limit, so exactly half of all the dogs reached the finish line on time. How many pairs and how many triples competed in the race?

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