
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 that \(\lambda\) is a positive real number and the sequence \(\left\{a_{n}\right\}\) satisfies:

\[a_{1}=\frac{1}{3}, \quad a_{n+1}=\frac{2 a_{n}^{2}}{4 a_{n}^{2}-2 a_{n}+1}, \quad n=1,2,3, \cdots\]

If for any \(m \in \mathbf{N}^{*}\), the inequality \(\sum_{k=1}^{m} a_{k}<\lambda\) holds, determine the minimum value of \(\lambda\).

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