
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

Today is January 30th, so we first write down 130. The rule for writing subsequent numbers is: if the last number written is even, divide it by 2 and then add 2; if the last number written is odd, multiply it by 2 and then subtract 2. Thus the sequence obtained is: $130, 67, 132, 68, \cdots$. What is the 2016th number in this sequence?

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