
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 decides to increase profit through two measures: increased investment in advertising and technological renovation. Market predictions suggest that for both investments not exceeding 3 million yuan, an advertising investment of x million yuan can approximately lead to an increase in sales volume computed by the function $y_{1}=-2x^{2}+14x$ (in million yuan). Similarly, a technological renovation investment of x million yuan can lead to an increase in sales volume approximated by the function $y_{2}=-\frac{1}{3}x^{3}+2x^{2}+5x$ (in million yuan). If the company invests 3 million yuan in total, divided between advertising and technological renovations, the predicted maximum increase in profit (Profit = Sales Volume - Investment) is \_\_\_\_\_ million yuan.

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