
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
Consider the following assertions:
(1) The function $y=\tan x$ is monotonically increasing within its domain.
(2) If $\alpha$ and $\beta$ are acute angles of the inner angle in triangle $\triangle ABC$, then $\sin \alpha > \cos \beta$.
(3) The axis of symmetry for the function $y=\cos \left( \frac{1}{2}x + \frac{3\pi}{2} \right)$ is $x=\frac{\pi}{2}+k\pi$, where $k \in \mathbb{Z}$.
(4) The graph of the function $y=\sin 2x$ shifted left by $\frac{\pi}{4}$ units produces the graph of $y=\sin(2x+\frac{\pi}{4})$.
The correct assertions are marked by the numbers \_\_\_\_\_\_.

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