
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
If $x_1$, $x_2$, $x_3$, $x_4$, $x_5$ are distinct positive odd numbers that satisfy $(2005-x_1)(2005-x_2)(2005-x_3)(2005-x_4)(2005-x_5) = 24^2$, determine the last digit of $x_1^2+x_2^2+x_3^2+x_4^2+x_5^2$.

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