
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 propositions, the true ones are (write down the serial numbers of all true propositions):
① Two functions that are inverse to each other have the same monotonicity;
② The graph of $y=f(x)$ is symmetric to the graph of $y=-f(-x)$ with respect to the origin;
③ An odd function $f(x)$ must have an inverse function $f^{-1}(x)$.

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