
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 that both sequences $\{a\_n\}$ and $\{b\_n\}$ are arithmetic sequences, and they satisfy $a\_5+b\_5=3$, $a\_9+b\_9=19$, find $a\_{100}+b\_{100}$ \_\_\_\_\_\_.

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