
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 the sequence \(\{a_n\}\) with the sum of the first \(n\) terms \(S_n\) and \(a_1 = \frac{1}{5}\), for any positive integers \(m\) and \(n\), \(a_{m+n} = a_m a_n\). If \(S_n < a\) holds for any \(n \in \mathbf{Z}_{+}\), find the minimum value of the real number \(a\).

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