
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 constant \\(p > 0\\), the sequence \\(\{a_n\}\\) satisfies \\(a_{n+1}=|p-a_n|+2a_n+p\\), where \\(n \in \mathbb{N}^*\\).
\\((1)\\) If \\(a_1=-1\\) and \\(p=1\\),
\\(①\\) Find the value of \\(a_4\\);
\\(②\\) Find the sum of the first \\(n\\) terms of the sequence \\(\{a_n\}\\), \\(S_n\\);
\\((2)\\) If there exist three terms \\(a_r\\), \\(a_s\\), \\(a_t (r, s, t \in \mathbb{N}^*, r < s < t)\\) in the sequence \\(\{a_n\}\\) that form an arithmetic sequence in order, find the range of values for \\(\frac{a_1}{p}\\).

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