
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
Princeton’s Math Club recently bought a stock for  $\$ 2 $ and sold it for $ \ $9$  thirteen days later. Given that the stock either increases or decreases by  $\$ 1 $ every day and never reached $ \ $0$ , in how many possible ways could the stock have changed during those thirteen days?


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