
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
For any positive real numbers \(a_1, a_2, \cdots, a_5\), if \(\sum_{i=1}^{5} \frac{a_i}{\sqrt{a_i^2 + 2^{i-1} a_{i+1} a_{i+2}}} \geq \lambda\), find the maximum value of \(\lambda\).

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