
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
Two internet companies, Company A and Company B, both had a market share of $A$ in 1996. According to market analysis and predictions, the market share of Company A in the $n$-th year (1996 being the 1st year) is given by $a_{n}=\frac{A}{40}\left(n^{2}-n+40\right)$. The market share of Company B has increased annually since 1996, following a certain pattern as shown in a provided graph.

1. Observing the graph, determine the expression for the market share of Company B in the $n$-th year.
2. According to the local market rules, if a company's market share is less than 20% of the other company's market share, the former will be merged by the latter. It has been calculated that there will be no mergers before 2015. Will there be a merger in 2015? Provide a detailed explanation.

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