
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
Josh buys $5$ cookies and $3$ cupcakes, paying a total of $23$ dollars, and Emily purchases $4$ cookies and $4$ cupcakes and spends $21$ dollars total; assuming cookies and cupcakes have constant prices, determine the ratio of the price of a cupcake to the price of a cookie.

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