
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
To find the value of $1+3+3^{2}+3^{3}+\cdots +3^{100}$, let $M=1+3+3^{2}+3^{3}\cdots +3^{100}$, then $3M=3+3^{2}+3^{3}+3^{4}+\cdots 3^{101}$, so $3M-M=3^{101}-1$, thus $M=\frac{{3^{101}}-1}{2}$, which means $1+3+3^{2}+3^{3}\cdots +3^{100}=\frac{{3^{101}}-1}{2}$. Following the above reasoning, calculate the value of $1+5+5^{2}+5^{3}+\cdots +5^{2023}$.

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