
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 $f(x)= \begin{cases}x^{2}-4x+3,x\leqslant 0 \\ -x^{2}-2x+3,x > 0\\ \end{cases}$, the inequality $f(x+a)\geqslant f(2a-x)$ always holds when $x∈[-2,2]$. Find the minimum value of the real number $a$.

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