
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
According to the rules of exponentiation, we have derived a new operation. The table below shows a set of examples corresponding to the two operations:<br/>

| Exponentiation | $2^{1}=2$ | $2^{2}=4$ | $2^{3}=8$ | $\ldots $ | $3^{1}=3$ | $3^{2}=9$ | $3^{3}=27$ | $\ldots $ |
|----------------|-----------|-----------|-----------|-----------|-----------|-----------|------------|-----------|
| New Operation  | $\log _{2}2=1$ | $\log _{2}4=2$ | $\log _{2}8=3$ | $\ldots $ | $\log _{3}3=1$ | $\log _{3}9=2$ | $\log _{3}27=3$ | $\ldots $ |

According to the above table, a student wrote three expressions: ①$\log _{2}16=4$, ②$\log _{5}25=5$, ③$\log _{3}81=4$. The correct one is ______ (fill in the number).

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