
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
The current population of a certain city is 1 million people. If the annual natural growth rate is 1.2%, please answer the following questions:
(1) Write the function relationship between the total population \(y\) (in tens of thousands) and the number of years \(x\);
(2) Calculate the total population of the city after 10 years (accurate to 0.1 tens of thousands);
(3) Calculate approximately how many years it will take for the city's population to reach 1.2 million (accurate to 1 year). \(1.012^{10} = 1.127\), \(1.012^{15} = 1.196\), \(1.012^{16} = 1.210\).

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