
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
Let the sequence $\{a_n\}$ have a sum of the first $n$ terms denoted as $S_n$, and define $T_n=\frac{S_1+S_2+\cdots +S_n}{n}$ as the "ideal number" of the sequence $a_1,a_2,\cdots,a_n$. It is known that the "ideal number" of the sequence $a_1,a_2,\cdots,a_{504}$ is 2020. Determine the "ideal number" of the sequence $2,a_1,a_2,\cdots,a_{504}$.

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