
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 descriptions and domains of five functions, marked as (1) through (5), determine which are invertible. Here are brief descriptions:
1. Function (1) has a domain of $$\{-6, -5, -4, -3, -2, -1, 0, 1\}$$ and is represented by a set of ordered pairs, all unique.
2. Function (2) represents a quadratic, $$f(x) = x^2 - 3x + 2$$ with a domain of $$[-3, 3]$$. 
3. Function (3) is modeled with $$f(x) = 1/x$$, and its domain prevents it from having a zero denominator; $$x \in [-8, -0.5] \cup [0.5, 8]$$. 
4. Function (4) is represented by $$f(x) = \sin(x)$$ with a domain of $$[0, \pi]$$.
5. Function (5) describes a linear function $$f(x) = 2x + 1$$ with a domain of $$\mathbb{R} \setminus \{1\}$$ (all reals except 1).

Identify and multiply the labels of the invertible functions.

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