
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
A certain manufacturer promises that during a promotional period, 3 empty cans of their brand of cola can be exchanged for 1 can of cola. Regarding this promotion, the following three statements are made:<br/>① If you buy 10 cans of cola, you can actually drink at most 13 cans of cola;<br/>② To drink 100 cans of cola, you need to buy at least 67 cans of cola;<br/>③ If you buy $n$ ($n\in N^{*}$) cans of cola, then the maximum number of cans of cola that can actually be consumed is $f(n)=n+[\frac{{n-1}}{2}]$. (where $[x]$ represents the largest integer not greater than $x$)<br/>The correct statements are numbered as ____.

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