
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 common ratio of the geometric sequence $\{a_n\}$ is $q$, and the product of its first $n$ terms is $T_n$. It also satisfies the conditions $a_1 > 1$, $a_{99}a_{100}-1 > 0$, and $\frac{a_{99}-1}{a_{100}-1} < 0$. Among the following conclusions:

$① 0 < q < 1$;

$② a_{99}a_{101}-1 < 0$;

$③ T_{100}$ is the maximum value among all $T_n$;

$④$ The largest natural number $n$ that makes $T_n > 1$ is equal to $198$.

The correct conclusions are __.

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