
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 the sequence $\{a_n\}$ is an arithmetic sequence, and $c_n = a_n^2 - a_{n+1}^2$ ($n \in \mathbb{N}^*$),

(1) Determine whether the sequence $\{c_n\}$ is an arithmetic sequence, and explain the reason;

(2) If $a_1 + a_3 + \ldots + a_{25} = 130$, $a_2 + a_4 + \ldots + a_{26} = 117$, find the common difference $d$ and the general formula of the sequence $\{a_n\}$.

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