
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
The real numbers \( a_{1}, a_{2}, \ldots, a_{16} \) fulfill the two conditions

\[ \sum_{i=1}^{16} a_{i}=100 \quad \text{and} \quad \sum_{i=1}^{16} a_{i}^{2}=1000 \]

What is the largest possible value that \( a_{16} \) can take?

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