
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
Two dogs and a cat together weigh 36 pounds. The heavier dog and the cat together weigh exactly three times as much as the lighter dog, and the lighter dog and the cat together weigh exactly twice as much as the heavier dog. How much does the lighter dog weigh?

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