
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 clever rabbit and the foolish fox make an agreement: every time the fox passes the bridge in front of the rabbit’s house, the rabbit will give the fox money, making the fox’s money double. However, each time the fox crosses the bridge, it has to pay the rabbit a crossing fee of $2^{2019}$ cents. The fox is very happy to hear that its money will double each time it crosses the bridge, but after crossing the bridge 2019 times, it realizes that all its money has been given to the rabbit. How much money did the fox initially have?

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