
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 company sells a brand of cars in two locations, A and B, with profits (unit: 10,000 yuan) represented by $L_1 = 5.06x - 0.15x^2$ and $L_2 = 2x$, respectively, where $x$ is the number of cars sold. If the company sells a total of 15 cars in both locations, find the maximum profit they can obtain.

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