
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

For a natural number \( n > 0 \), consider an operation " \( G \)" defined as:
(1) If \( n \) is odd, \( G(n)=3n+1 \);
(2) If \( n \) is even, \( G(n) \) is obtained by dividing \( n \) by 2 continuously until the quotient is odd.

Let \( G^k \) denote performing the operation \( G \) \( k \) times. For example, \( G^1(5) = 3 \times 5 + 1 = 16 \), \( G^2(5) = G^1(16) = 16 \div 2 \div 2 \div 2 \div 2 = 1 \), \( G^3(5) = 3 \times 1 + 1 = 4 \), \( G^4(5) = 4 \div 2 \div 2 = 1 \).

Calculate:
(1) The value of \( G^1(2016) \);
(2) The value of \( G^5(19) \);
(3) The value of \( G^{2017}(19) \).

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