
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]


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A certain factory's annual fixed cost for a type of product is 2.5 million yuan, and the additional cost incurred for producing \(x\) thousand units of this product is \(G(x)\) (unit: ten thousand yuan). When the annual output is less than 80 thousand units, \(G(x) = \frac{1}{3}x^{2} + 10x\); when the annual output is not less than 80 thousand units, \(G(x) = 51x + \frac{10,000}{x} - 1,450.\) It is known that the selling price per unit of the product is 0.05 million yuan. Through market analysis, it is determined that the factory can sell all the products it produces. The maximum annual profit that the factory can obtain from producing this product is \_\_\_\_\_\_\_\_ million yuan.

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