
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 sum of the prices of 4 roses and 5 peonies in a flower shop is not less than 27 yuan, while the sum of the prices of 6 roses and 3 peonies does not exceed 27 yuan. What is the maximum sum of the prices for 3 roses and 4 peonies in this flower shop?

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