
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
(1) In the sequence $\left\{a_{n}\right\}$,

\[a_{1}=1, \quad a_{n+1}=\frac{10+4 a_{n}}{1+a_{n}} \quad (n \in \mathbf{Z}_{+})\]

find the general term formula of the sequence $\left\{a_{n}\right\}$.

(2) Given the sequence $\left\{a_{n}\right\}$ satisfies:

\[a_{1}=2, \quad a_{n+1}=\frac{a_{n}-1}{a_{n}+1} \quad (n \in \mathbf{Z}_{+})\]

find the value of $a_{2019}$.

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