
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 cars in locations A and B, with profits (in units of 10,000 yuan) of $L_{1}=5.06x-0.15x^{2}$ and $L_{2}=2x$ respectively, where $x$ is the sales volume (in units). If the company sells a total of 15 cars in these two locations, what is the maximum profit (in 10,000 yuan) the company can achieve?

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