
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 city is 1 million people. If the average annual natural growth rate is 1.2%,

(1) Write the function relationship between the city's total population $y$ (in millions) and the number of years $x$;  
(2) Calculate the total population of the city in 10 years (accurate to 0.1 thousand); (Reference data $1.012^{10} \approx 1.1267$)  
(3) Approximately how many years will it take for the city to reach a population of 1.2 million? (accurate to 1 year) (Reference data $\log_{1.012}1.2 \approx 15.3$)

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