
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 following propositions:

1. $y=\dfrac{1}{x}$ is a power function;
2. $\lg ({{x}^{2}}+\dfrac{1}{4}) > \lg x$ ($x > 0$);
3. The area of the shape formed by the graph of the function $y=\sin x$ ($x\in [0,\pi]$) and the $x$-axis is $2$;
4. If $\xi \sim N(1,{{\sigma}^{2}})$, and $P(0\leqslant \xi \leqslant 1)=0.3$, then $P(\xi \geqslant 2)=0.2$;
5. The term with the largest coefficient in the expansion of the binomial $({x}^{2}- \dfrac{1}{x})^{10}$ is the 6th term.

The sequence numbers of the true propositions are ________ (Write down all the correct proposition numbers).

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