
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 non-zero common difference $d$, an arithmetic sequence $\{a_n\}$ satisfies $a_1 = 2$, and $a_1, a_2, a_5$ form a geometric sequence.

(Ⅰ) Find the general term formula of the sequence $\{a_n\}$.

(Ⅱ) Let $S_n$ be the sum of the first $n$ terms of the sequence $\{a_n\}$. Find the smallest positive integer $n$ such that $S_n > 60n + 800$.

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