
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 four judgments:

1. If $f(x)=x^{2}-2ax$ is an increasing function on $[1,+\infty)$, then $a=1$;

2. The function $f(x)=2^{x}-x^{2}$ has only two zeros;

3. The function $y=2^{|x|}$ has a minimum value of $1$;

4. In the same Cartesian coordinate system, the graphs of the functions $y=2^{x}$ and $y=2^{-x}$ are symmetric about the $y$-axis.

The correct sequence numbers are __________.

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