
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
An arithmetic sequence $\{a_n\}$ with a non-zero common difference has 20 terms, with the first term being 5. The 1st, 4th, and 16th terms of this sequence are respectively the 1st, 3rd, and 5th terms of a positive geometric sequence $\{b_n\}$.

1. Find the general term formulas for $\{a_n\}$ and $\{b_n\}$.
2. Let $S$ denote the sum of all terms in $\{a_n\}$. Find the maximum value of $n$ such that $b_n \leq S$.

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