
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) > f(2a-x)\\) holds for all \\(x\\) in the interval \\([a,a+1]\\). Then, the range of the real number \\(a\\) is \_\_\_\_\_\_\_\_\_\_\_\_.

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