
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 the sequence \(\left\{a_{n}\right\}\) with the sum of the first \(n\) terms \(S_{n}=3n^{2}+5n\), and the geometric sequence \(\left\{b_{n}\right\}\) with \(b_{1}=8\) and \(64b_{n+1}-b_{n}=0\), there exists a constant \(c\) such that for any positive integer \(n\), \(a_{n+1}+\log_{c} b_{n}\) is a constant \(m\). Find the values of the constants \(c\) and \(m\).

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