
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 $p$: The solution set of the inequality $(a-1)^x > 1$ is $\{x|x<0\}$, and $q$: $a^2 - 2ta + t^2 - 1 < 0$, if $\neg p$ is a necessary but not sufficient condition for $\neg q$, find the range of the real number $t$.

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