
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 an arithmetic sequence $\{a_n\}$, the first term $a_1 = 0$ and the common difference $d \neq 0$, determine the value of $k$ such that the sum of the first seven terms $a_1 + a_2 + \ldots + a_7 = a_k$.

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