
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
Compute the number of ordered quintuples of nonnegative integers  $(a_1,a_2,a_3,a_4,a_5)$  such that  $0\leq a_1,a_2,a_3,a_4,a_5\leq 7$  and  $5$  divides  $2^{a_1}+2^{a_2}+2^{a_3}+2^{a_4}+2^{a_5}$ .

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