
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
An expression like
$$
x=1+\frac{1}{2+\frac{1}{3+\frac{1}{4}}}
$$
is called a continued fraction.

1. Write \( x \) given above as a reduced fraction of the form \( \frac{a}{b} \) where \( a \) and \( b \) are positive integers.

2. Write \( \frac{355}{113} \) as a continued fraction in the form \( a+\frac{1}{b+\frac{1}{c}} \), where \( a, b, c \) are positive integers.

3. Let
$$
y=8+\frac{1}{8+\frac{1}{8+\frac{1}{8+\cdots}}}
$$
where the process continues indefinitely. Given that \( y \) can be written in the form \( p+\sqrt{q} \), find the integers \( p \) and \( q \).

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