
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 four propositions:  
(1) Using a random draw method, each individual has an equal chance of being selected;  
(2) Using Qin Jiushao's algorithm
  
  $$
  \begin{cases}
    v_{0} = a_{n} \\
    v_{k} = v_{k-1}x + a_{n-k} & (k=1,2,\cdots,n)
  \end{cases}
  $$
  to calculate the value of the polynomial $f(x) = x^5 + 2x^3 - x^2 + 3x + 1$ at $x=1$, we have $v_3 = 2$;  
(3) The statement "-3 < m < 5" is a necessary but not sufficient condition for the equation $\frac{x^2}{5-m} + \frac{y^2}{m+3} = 1$ to represent an ellipse;  
(4) There exists $a \in \mathbb{R}$ such that for all $x \in \mathbb{R}$, $x^2 + 2x + a < 0$.  
Among these, the true propositions are ___________ (fill in the numbers).

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