
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
Consider the set of all ordered  $6$ -tuples of nonnegative integers  $(a,b,c,d,e,f)$  such that \[a+2b+6c+30d+210e+2310f=2^{15}.\] In the tuple with the property that  $a+b+c+d+e+f$  is minimized, what is the value of  $c$ ?


*2021 CCA Math Bonanza Tiebreaker Round #1*

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