
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 function $f(x) = |2^x - 1|$, and $a < b < c$, with $f(a) > f(c) > f(b)$, which of the following statements must be true?  
① $a < 0$, $b < 0$, $c < 0$; ② $a < 0$, $b \geq 0$, $c > 0$; ③ $2^{-a} < 2^c$; ④ $2^a + 2^c < 2$.

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