
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 that $\{ a_n \}$ is an arithmetic sequence with a non-zero common difference $d$. If $a_2$, $a_3$, and $a_7$ form a geometric sequence, and $2a_1 + a_2 = 1$, find the general term $a_n$.

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