
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]


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A factory's monthly production of a certain product in the first quarter was 100,000 units, 120,000 units, and 130,000 units, respectively. To predict the monthly production for the following months, based on the production of these three months, a function is used to simulate the relationship between the monthly production $y$ (in units of 100,000) and the month $x$. Simulation function 1: $y=ax+ \frac{b}{x}+c$; Simulation function 2: $y=mn^x+s$.  
(1) Given that the production in April was 137,000 units, which function should be chosen as the simulation function?  
(2) Due to the influence of factory equipment, the monthly production throughout the year does not exceed 150,000 units. Please choose the appropriate simulation function to predict the production in June.

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