
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
Among the following four propositions about conic sections:  
(1) The two real roots of the equation $2x^2-5x+2=0$ can be used as the eccentricities of an ellipse and a hyperbola, respectively;  
(2) Let $A$ and $B$ be two fixed points on a plane, if $|PA| - |PB| = k (k>0)$, the locus of point $P$ is a hyperbola;  
(3) If the equation $kx^2+(4-k)y^2=1$ represents an ellipse, then the range of $k$ is $(0,4)$;  
(4) The hyperbola $ \frac {x^2}{25}- \frac {y^2}{9}=1$ and the ellipse $ \frac {x^2}{35}+y^2=1$ have the same foci.  
Please write down the serial numbers of all true propositions.

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