
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 $\triangle ABC$, where $A(-2,0)$, $B(2,0)$, $C(x,1)$,
(i) If $\angle ACB$ is a right angle, then $x=$ \_\_\_\_\_\_
(ii) If $\triangle ABC$ is an acute triangle, then the range of $x$ is \_\_\_\_\_\_.

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