
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. "The equation ${{x}^{2}}-4x-5=0$" has a necessary but not sufficient condition "$x=5$";
2. For the propositions $p: \exists x \in \mathbb{R}, \tan x = 1$ and $q: \forall x \in \mathbb{R}, {{x}^{2}}-x+1 > 0$, the proposition "$p \wedge (\neg q)$" is false;
3. The equation of the tangent line to the function $f(x)={{x}^{3}}-3{{x}^{2}}+1$ at the point $(2,f(2))$ is $y=-3$.

The correct proposition numbers are ______.

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