
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
If real numbers $x$, $y$, $m$ satisfy $|x-m| < |y-m|$, then $x$ is said to be closer to $m$ than $y$.  
(1) If $x^2$ is closer to 1 than 4, find the range of $x$.  
(2) When $a > 0$, if $x^2 + a$ is closer to 0 than $(a+1)x$, find the range of $x$.

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