
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 shopkeeper has a $\$20$ hat and a $\$15$ tie. He decides to discount the hat by $25\%$ and later by $20\%$ of the reduced price. For the tie, he gives an initial discount of $10\%$ followed by an additional $30\%$ of the new price. What are the final prices of the hat and the tie?

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