
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
Let there be  $A=1^{a_1}2^{a_2}\dots100^{a_100}$  and  $B=1^{b_1}2^{b_2}\dots100^{b_100}$  , where  $a_i , b_i \in N$  ,  $a_i + b_i = 101 - i$  , ( $i= 1,2,\dots,100$ ). Find the last 1124 digits of  $P = A * B$ .

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