
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 $a\in \left[-1,1\right]$, the function $f\left(x\right)=\left\{\begin{array}{l}\sin\left[2\pi\right(x-a\left)\right],x≤a,\\{x}^{2}-2(a+1)x+{a}^{2},x>a.\end{array}\right.$ If $f\left(f\left(a\right)\right)=1$, then $a=$____.

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