
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
Define the operation $○\llap{×}$ on $\mathbb{R}$ as: $x ○\llap{×} y = x(1-y)$. If the inequality $(x-a)○\llap{×}(x+a) < 2$ holds true for all real numbers $x \in [1,2]$, then the range of $a$ is \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

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