
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
A game involves jumping to the right on the real number line. If  $ a$  and  $ b$  are real numbers and  $ b>a,$  the cost of jumping from  $ a$  to  $ b$  is  $ b^3\minus{}ab^2.$  For what real numbers  $ c$  can one travel from  $ 0$  to  $ 1$  in a finite number of jumps with total cost exactly  $ c?$ 

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