
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]


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Given a function \\(f(x)\\) defined on \\(\mathbb{R}\\) that satisfies: \\(①f(1+x)=f(1-x)\\); \\(②\\) is an increasing function on \\([1,+\infty)\\). If for \\(x \in \left[\frac{1}{2},1\right]\\), the inequality \\(f(ax) < f(x-1)\\) holds, then the range of the real number \\(a\\) is \_\_\_\_\_\_\_.

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