
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
Chuck and Huck were decorating the Christmas tree. To prevent them from arguing, their mom allocated the same number of branches and the same number of ornaments to each of them. Chuck tried to hang one ornament on each branch, but he was short one branch. Huck tried to hang two ornaments on each branch, but one branch remained empty. How many branches and how many ornaments did their mom allocate to the sons?

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