
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 the same brand of car in locations A and B, with profits (in tens of thousands of yuan) being $L_1 = 5.06x - 0.15x^2$ and $L_2 = 2x$ respectively, where $x$ is the number of cars sold. If the company sold a total of 15 cars between these two locations, what is the maximum profit (in tens of thousands of yuan) that the company can achieve?

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