
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 $\{a_n\}$ (where $n \in \mathbb{N}^*$) with the first term $a_1 = 1$, and $a_1$, $a_2$, $a_4$ form a geometric sequence, find the value of $a_4 + a_8 + a_{12} + \ldots + a_{4n+4}$.

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