
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 sequences \(\{a_n\}\) and \(\{b_n\}\) are both arithmetic sequences, and the sequence \(\{c_n\}\) is defined by \(c_n = a_n b_n\) (for \(n \in \mathbb{N}^*\)). If \(c_1 = 1440\), \(c_2 = 1716\), and \(c_3 = 1848\), find the value of \(c_8\).

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