
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 hyperbola $\frac{x^2}{25} - \frac{y^2}{9} = 1$ and the ellipse $\frac{x^2}{35} + y^2 = 1$ have the same foci;
2. $(\ln x)' = \frac{1}{x \ln e}$;
3. $(\tan x)' = \frac{1}{\cos^2 x}$;
4. $\left(\frac{u}{v}\right)' = \frac{uv' - vu'}{v^2}$;
5. For all $x \in \mathbb{R}$, $x^2 - 3x + 3 \neq 0$.

Among these, the true propositions are: ______. (Fill in the numbers of all correct propositions)

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