
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 monotonic function $f(x)$ defined on $\mathbb{R}$, there exists a real number $x$ such that for any real numbers $x_1$, $x_2$, it always holds that $f(xx_1 + xx_2) = f(x) + f(x_1) + f(x_2)$. Then, (i) the value of $f(1) + f(0)$ is     (ii) the value of $x$ is     .

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