
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
Let \\( \{a_n\} \\) be a sequence with the sum of the first \\( n \\) terms denoted as \\( S_n \\). If \\( S_2 = 4 \\) and \\( a_{n+1} = 2S_n + 1 \\) where \\( n \in \mathbb{N}^* \\), find the values of \\( a_1 \\) and \\( S_5 \\).

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