
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 sequences \(\{a_n\}\) and \(\{b_n\}\) where \(a_1 = b_1 = 10\), the recursive formulas are defined as:
\[
\begin{cases}
a_{n+1} = \frac{1}{a_n b_n} \\
b_{n+1} = a_n^4 b_n
\end{cases} \quad (n \in \mathbb{Z}^+)
\]
Find \(a_n\) and \(b_n\).

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