
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
Bonus Question  
(1) Given the equation $|x^2-1|=a|x-1|$ has only one real solution, then the range of the real number $a$ is ______.  
(2) Let $\lfloor x \rfloor$ be the greatest integer less than or equal to $x$, then $\lfloor \log_{3}1 \rfloor + \lfloor \log_{3}2 \rfloor + \lfloor \log_{3}3 \rfloor + \ldots + \lfloor \log_{3}100 \rfloor =$ ______.

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