
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
The following statements are given:
1. $y=\tan x$ is an increasing function within its domain;
2. The smallest positive period of $y=\sin |2x+\frac{\pi}{6}|$ is $\pi$;
3. Given vectors $\overrightarrow{a}=(2,\lambda)$ and $\overrightarrow{b}=(-3,5)$, and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is obtuse, the range of $\lambda$ is $(-\infty,\frac{6}{5})$;
4. For the function $y=a+2\cdot 2^x+4^x$, when $x\in(-\infty,1]$, $y<0$ always holds, then $a<-8$.
Determine the correct statement(s).

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