
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
We say "$s$ grows to $r$" if there exists some integer \( n > 0 \) such that \( s^n = r \). Call a real number \( r \) "sparse" if there are only finitely many real numbers \( s \) that grow to \( r \). Find all real numbers that are sparse.

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