
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
The sequence $a_n$ is an arithmetic sequence with a common difference $d$ not equal to 0, and $a_{2046} + a_{1978} - a_{2012}^2 = 0$. The sequence $b_n$ is a geometric sequence, and $b_{2012} = a_{2012}$. Find the value of $b_{2010} \cdot b_{2014}$.

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