
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 annual natural growth rate is 1.2%,
(1) Write the function relationship between the total population of the city (in ten thousand) and the number of years;
(2) Calculate approximately how many years later the population of the city will reach 1.2 million (accurate to 1 year);
(3) If the total population of the city does not exceed 1.2 million in 20 years, what should the annual natural growth rate be controlled at? (Given that $\lg 1.2 \approx 0.079$, $\lg 1.012 \approx 0.005$, $\lg 1.009 \approx 0.0039$)

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