
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
For the sequence $\left\{a_{n}\right\}$, let $b_{n}=a_{n+1}-a_{n}$, then the sequence $\left\{b_{n}\right\}$ is the first-order difference sequence of $\left\{a_{n}\right\}$. Let $c_{n}=b_{n+1}-b_{n}$, then the sequence $\left\{c_{n}\right\}$ is the second-order difference sequence of $\left\{a_{n}\right\}$. By analogy, we can obtain the $p$-th order difference sequence of $\left\{a_{n}\right\}$. If the $p$-th order difference sequence of $\left\{a_{n}\right\}$ is a non-zero constant sequence, then $\left\{a_{n}\right\}$ is called a $p$-th order arithmetic sequence. Given that the sequence $\left\{a_{n}\right\}$ is a second-order arithmetic sequence, $a_{10}=23, a_{20}=23$, and in the second-order difference sequence $\left\{c_{n}\right\}$, $c_{n}=20$, find $a_{30}=$ ______.

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