
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 that the sum of the first 5 terms of an arithmetic sequence \\(\\{a\_{n}\\}\\) is \\(105\\), and \\(a\_{10}=2a\_{5}\\).
\\((\\)Ⅰ\\()\\) Find the general term formula of the sequence;
\\((\\)Ⅱ\\()\\) For any \\(m∈N^{\*}\\), let \\(b\_{m}\\) denote the number of terms in the sequence \\(\\{a\_{n}\\}\\) that are not greater than \\(7^{2m}\\). Find the sum of the first \\(m\\) terms of the sequence \\(\\{b\_{m}\\}\\), denoted as \\(S\_{m}\\).

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