
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
The sequence  $ (a_n)$  is given by  $ a_1\equal{}1,a_2\equal{}0$  and:

 $ a_{2k\plus{}1}\equal{}a_k\plus{}a_{k\plus{}1}, a_{2k\plus{}2}\equal{}2a_{k\plus{}1}$  for  $ k \in \mathbb{N}.$ 

Find  $ a_m$  for  $ m\equal{}2^{19}\plus{}91.$ 

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