
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 $p:f(x)=\frac{1-x}{3}$ and $|f(a)| < 2$; $q$: the set $A=\{x|x^2+(a+2)x+1=0, x \in \mathbb{R}\}$, and $A \neq \varnothing$. If $p \vee q$ is a true proposition, and $p \wedge q$ is a false proposition, find the range of the real number $a$.

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