
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
Given that a city had a total population of 2 million at the end of 2015, and assuming that the annual growth rate of the city's population is 1% thereafter (not considering other factors),
(1) If after x years the total population of the city is y (in ten thousands), write the functional relationship between y and x;
(2) If the city's total population reaches 2.1 million, how many years (rounded up to the nearest whole year) is needed at least?

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