
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 certain supermarket's monthly sales from January to December in 2017 showed a trend of first decreasing and then increasing. There are three function models:

1. $f(x)=p \cdot q^{x} \quad (q > 0, q \neq 1)$;
2. $f(x)=\log_{p}x + q \quad (p > 0, p \neq 1)$;
3. $f(x)=x^{2} + px + q$.

(a) The function model that can more accurately reflect the relationship between the supermarket's monthly sales $f(x)$ and the month $x$ is _________.

(b) If the selected function satisfies $f(1)=10$ and $f(3)=2$, then the minimum value of $f(x)$ is _________.

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