
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
Given that the domain of the function $f(x)$ is ${x|x≠kπ,k∈Z}$, and for any $x$, $y$ in the domain, $f(x−y)=\frac{f(x)⋅f(y)+1}{f(y)−f(x)}$ holds. Also, $f(a)=1$ ($a$ is a positive constant), and $f(x) > 0$ when $0 < x < 2a$.

1. Determine the parity of $f(x)$.
2. Find the minimum and maximum values of $f(x)$ on the interval $[2a,3a]$.

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