
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
A positive integer  $k$  is called *powerful* if there are distinct positive integers  $p, q, r, s, t$  such that  $p^2$ ,  $q^3$ ,  $r^5$ ,  $s^7$ ,  $t^{11}$  all divide k. Find the smallest powerful integer. 

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