
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 $a$ and $b$ that satisfy the system of equations:
$$
\begin{cases}
4a-3b=22 \\
2a+b=16
\end{cases}
$$
(1) Find the values of $a$ and $b$;
(2) If $a$ and $b$ are two side lengths of an isosceles triangle, find the perimeter of this triangle.

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