
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 function $f(x)$ for any $x, y \in \mathbb{R}$, it satisfies $f(x) + f(y) = f(x+y)$.
1. Find the value of $f(0)$;
2. Determine the parity of $f(x)$;
3. If $f(1) = 1$, and $f(x)$ is an increasing function on $[0, +\infty)$, find the range of $x$ that satisfies the inequality $f(2^x - x) + f(x) > 4$.

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