
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 \( p \): function \( f(x)=\log _{a} x (x>0) \) is monotonically increasing; Proposition \( q \): function \( g(x)=x^{2} + a x + 1 > 0 \) \( (x \in \mathbf{R}) \). If \( p \vee q \) is true and \( p \wedge q \) is false, find the range of the real number \( a \).

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