
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 the sequence $\{a\_n\}$ that satisfies: $a_{4n-3}=1$, $a_{4n-1}=0$, $a_{2n}=a_{n}$, where $n\in\mathbb{N}^*$, determine the values of $a_{2009}=$ \_\_\_\_\_\_ and $a_{2004}=$ \_\_\_\_\_\_.

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