
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 the curve $C:\begin{cases}x=\frac{\sqrt{2}}{2}t\\y=a+\frac{\sqrt{2}}{2}t\end{cases}$ (with $t$ as the parameter), points $A(-1,0)$, and $B(1,0)$, determine the range of values for the real number $a$ if there exists a point $P$ on curve $C$ such that $\overrightarrow{AP}\cdot\overrightarrow{BP}=0$.

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