
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
Find the general term for the following recurrence sequences:
$$
\begin{array}{l}
\text{(1) } a_{1}=\frac{1}{2}, a_{n+1}=\frac{a_{n}+3}{2a_{n}-4} \text{ for } n \geq 1; \\
\text{(2) } a_{1}=5, a_{n+1}=\frac{a_{n}-4}{a_{n}-3} \text{ for } n \geq 1.
\end{array}
$$

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