
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 the value of  $1^{25}+2^{24}+3^{23}+\ldots+24^2+25^1$ .  If your answer is  $A$  and the correct answer is  $C$ , then your score on this problem will be  $\left\lfloor25\min\left(\left(\frac AC\right)^2,\left(\frac CA\right)^2\right)\right\rfloor$ .

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