
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 the proposition $p: \forall x \in (-\infty, 0)$, $3^x < 4^x$; proposition $q$: If matrix $A = \begin{bmatrix} 1 & 0 \\ -1 & 1 \end{bmatrix}$, then $A^n = \begin{bmatrix} 1 & 0 \\ -n & 1 \end{bmatrix} (n \in \mathbb{N}^*)$. Among the following propositions: $① p \wedge q$; $② p \vee (\neg q)$; $③ p \wedge (\neg q)$; $④ (\neg p) \wedge q$. There are $\_\_\_\_\_\_\_\_$ true propositions.

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