
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 $r, s, t$ be integers, and consider the set $\{x \mid x=2^r+2^s+2^t, 0 \leq t < s < r\}$. The numbers in this set, arranged in increasing order, form a sequence $\{a_n\}$. If $a_1=7$, $a_2=11$, $a_3=13$, $a_4=14$, ..., find the value of $a_{36}$.

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