
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
Nine positive integers  $a_1,a_2,...,a_9$  have their last  $2$ -digit part equal to  $11,12,13,14,15,16,17,18$  and  $19$  respectively. Find the last  $2$ -digit part of the sum of their squares.

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