
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
Emily starts with an empty bucket. Every second, she either adds a stone to the bucket or removes a stone from the bucket, each with probability  $\frac{1}{2}$ . If she wants to remove a stone from the bucket and the bucket is currently empty, she merely does nothing for that second (still with probability  $\hfill \frac{1}{2}$ ). What is the probability that after  $2017$  seconds her bucket contains exactly  $1337$  stones?

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