
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 propositions: 
- $①(\log_{a}x)'= \frac{1}{x\ln x}$;
- $②(\cos x)'=-\sin x$;
- $③\left( \frac{u}{v}\right)'= \frac{uv'-vu'}{v^{2}}$;

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

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