
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 $a > 0$, $b > 0$ and $2ab = a + 2b + 3$.
(1) Find the minimum value of $a + 2b$;
(2) Determine whether there exist $a$, $b$ such that $a^2 + 4b^2 = 17$, and explain the reason.

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