
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 that the function $f(x)$ satisfies $f(x+y)=f(x)+f(y)$ for all $x, y \in \mathbb{R}$, and $f(x) > 0$ when $x > 0$, $f(1)=2$.

1. Find the values of $f(0)$ and $f(3)$.
2. Determine the monotonicity of $f(x)$.
3. If $f(4^{x}-a)+f(6+2^{x+1}) > 6$ holds for all $x$, find the range of values for the real number $a$.

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