
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
Determine the true statements among the following propositions:
1. The function $y=x^2$ is a power function.
2. The zero point of the function $f(x)=x+\ln x$ is in the interval $(\frac{1}{e},1)$.
3. If point $D$ in $\triangle ABC$ satisfies $\overrightarrow{AD}=\lambda (\frac{\overrightarrow{AB}}{|\overrightarrow{AB}|}+\frac{\overrightarrow{AC}}{|\overrightarrow{AC}|})$, then point $D$ is on the bisector of $\angle BAC$.
4. The closer the absolute value of the linear correlation coefficient $r$ is to $1$, the weaker the linear correlation between the two variables.

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