
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 took some positive integer powers of a positive rational number.

What could this number have been if we can divide these powers into two groups such that the sum of the numbers in each group is equal?

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