
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:

(1) The graph of an even function always intersects with the $y$-axis;
(2) The graph of an odd function always passes through the origin;
(3) If the odd function $f(x) = a - \frac{2}{2^x + 1}$, then $a = 1$ as a real number;
(4) An odd function whose graph passes through the origin must be a monotonic function;
(5) The number of zeros of the function $y = 2^x - x^2$ is $2$;
(6) The graphs of two functions that are inverses of each other are symmetric about the line $y = x$.

Identify the sequence numbers of all correct propositions.

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