
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, along with their mother, were decorating the Christmas tree. To prevent them from fighting, their mother allocated an equal number of branches and an equal number of ornaments to each of the brothers. Chuck tried to hang one ornament on each branch but ended up one branch short. Huck tried to hang two ornaments on each branch, but one branch ended up empty. How many branches and how many ornaments did their mother allocate to each of the sons?

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