
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
Given $ a_{i} \in \left\{0,1,2,3,4\right\}$ for every $ 0\le i\le 9$ and $6 \sum _{i = 0}^{9}a_{i} 5^{i} \equiv 1\, \, \left(mod\, 5^{10} \right)$ , find the value of $ a_{9} $.

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