
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
Let  $a_n$  be a sequence with  $a_0=1$  and defined recursively by  $$ a_{n+1}=\begin{cases}a_n+2&\text{if }n\text{ is even},2a_n&\text{if }n\text{ is odd.}\end{cases} $$  What are the last two digits of  $a_{2015}$ ?

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