
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
Compute ${({\log_2 })^{20}} + C_{20}^1{({\log_2 })^{19}}{\log_5 } + \cdots + C_{20}^{r - 1}{({\log_2 })^{21 - r}}{({\log_5 })^{r - 1}} + \cdots + {({\log_5 })^{20}}$.

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