
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 an increasing arithmetic sequence ${a_{n}}(n∈N^{*})$ with the first term $a_{1}=1$, and $a_{1}$, $a_{2}$, $a_{4}$ form a geometric sequence, find the general term formula $a_{n}=$ ________ and the sum $a_{4}+a_{8}+a_{12}+…+a_{4n+4}=$ ________.

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