
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 five propositions, the numbers of the true propositions are __________ (write down the numbers of all true propositions).
(1) Given $$C: \frac {x^{2}}{2-m}+ \frac {y^{2}}{m^{2}-4}=1$$ (m∈R), when m＜-2, C represents an ellipse.  
(2) On the ellipse $$\frac {x^{2}}{45}+ \frac {y^{2}}{20}=1$$, there is a point P, F<sub>1</sub> and F<sub>2</sub> are the left and right foci of the ellipse, respectively, and △F<sub>1</sub>PF<sub>2</sub> is a right-angled triangle, then there are 8 such points P.  
(3) The curves $$\frac {x^{2}}{10-m}+ \frac {y^{2}}{6-m}=1 (m<6)$$ and $$\frac {x^{2}}{5-m}+ \frac {y^{2}}{9-m}=1 (5<m<9)$$ have the same focal distance.  
(4) The standard equation of a hyperbola with asymptote equations $$y=\pm \frac {b}{a}x (a>0,b>0)$$ is definitely $$\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1$$.  
(5) The focus of the parabola y=ax<sup>2</sup> is $$(0, \frac {1}{4a})$$.

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