
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
A biologist placed some lotus plants in a lake on New Year's Day. The lotus plants spread faster and faster in the lake. At the end of February, the area covered by the lotus plants was measured to be $24m^{2}$, and at the end of March, the area covered was measured to be $36m^{2}$. The relationship between the area covered by the lotus plants $y(m^{2})$ and the month $x$(month) can be modeled by two functions: $y=ka^{x}(k > 0,a > 1)$ and $y=px^{ \frac {1}{2}}+q(p > 0)$.

(I) Determine which function model is more suitable and find its analytical expression;
(II) Find the smallest month when the area covered by the lotus plants is more than 10 times the area when they were placed in the lake.

(Reference data: $\lg 2≈0.3010$, $\lg 3≈0.4771$)

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