
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 \(a_{1}=1\), \(a_{2}=\frac{5}{3}\), and the recurrence relation \(a_{n+2}=\frac{5}{3}a_{n+1}-\frac{2}{3}a_{n}\) for \( n \in \mathbf{N}^{*}\), find the general term \(a_{n}\) of the sequence \(\{a_{n}\}\).

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