
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
Let the universal set $U=\mathbb{R}$, and the function $f(x)=\lg(|x+1|+a-1)$, where $(a<1)$. The domain of $f(x)$ is denoted as $A$, and the set $B=\{x|\cos\pi x=1\}$. If the intersection of the complement of $A$ in $U$ and $B$ has exactly two elements, find the range of $a$.

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