
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
In a geometric sequence $\{a_n\}$ where each term is positive, $a_1=2$ and $a_2$, $a_4+2$, $a_5$ form an arithmetic sequence. Let $S_n$ be the sum of the first $n$ terms of the sequence $\{a_n\}$, then find the sum of the first 5 terms, $S_5$.

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