
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 $a$, $b$, $c \in \mathbb{R}$, the number of correct statements among the following four statements is ______.<br/>① If $ac^{2} \gt bc^{2}$, then $a \gt b$;<br/>② If $|a-2| \gt |b-2|$, then $\left(a-2\right)^{2} \gt \left(b-2\right)^{2}$;<br/>③ If $a \gt b \gt c \gt 0$, then $\frac{1}{a}＜\frac{1}{b}＜\frac{1}{c}$;<br/>④ If $ab\neq 0$, then $\frac{b}{a}+\frac{a}{b}≥2$.

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