
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 that $a\neq 0$ is a real number, the function $f(x)$ is defined as follows:
$$f(x)= \begin{cases} 2x+a,&x < 1 \\ -x-2a,&x\geqslant 1 \end{cases}$$
(1) If $a=-3$, find the values of $f(10)$ and $f(f(10))$;
(2) If $f(1-a)=f(1+a)$, find the value of $a$.

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