
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

The trunk of the sky-high tree branches into two at a height of one foot. We consider a branch to be the section between two consecutive nodes where no further branching occurs. Each branch in the sky-high tree is straight and ends one foot higher than the lower end. We refer to the branches emerging from the higher end of a branch as its children, and these branches are also referred to as each other's siblings.

Every branch in the sky-high tree has at least two children, and if it doesn't have exactly two children, then it has a sibling with exactly two children. Siblings always have different numbers of children. If a branch has more than two children, then it has a sibling with exactly one fewer child than itself. 

How many branches emerge from the nodes that are $n$ feet high?

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