
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 two propositions:

Proposition \( p \): The function \( f(x)=\log_{a} x \) (\( x > 0 \)) is monotonically increasing;
Proposition \( q \): The function \( g(x) = x^2 + ax + 1 > 0 \) (\( x \in \mathbf{R} \)).

If \( p \vee q \) is a true proposition and \( p \wedge q \) is a false proposition, then the range of the real number \( a \) is...

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