
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
At Flora's Flower Boutique, a bouquet containing 15 roses costs $\$30$. If the price of a bouquet is directly proportional to the number of roses it contains up to 30 roses, and any additional rose beyond 30 costs half the usual price per rose, how much will a bouquet of 50 roses cost?

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