
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 any $x\_1$ and $x\_2$ ($x\_1 \neq x\_2$) in the domain of the function $f(x)$, the following conclusions are drawn:
1. $f(0) = 1$;
2. $f(1) = 0$;
3. $f(x\_1 + x\_2) = f(x\_1) \cdot f(x\_2)$;
4. $f(x\_1 \cdot x\_2) = f(x\_1) + f(x\_2)$;
5. $f(\frac{x\_1 + x\_2}{2}) < \frac{f(x\_1) + f(x\_2)}{2}$;
6. $f(\frac{x\_1 + x\_2}{2}) > \frac{f(x\_1) + f(x\_2)}{2}$.
When $f(x) = 2^x$, which of the above conclusions are true? (Fill in the sequence numbers of all correct conclusions)

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