
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 sequences $\{a_n\}$ and $\{b_n\}$ satisfy $(a_1=1, a_2=3, b_1=5)$, and for any positive integers $i,j,k,l$, if $i+j=k+l$, then $(a_i+b_j=a_k+b_l)$. Find $(a_n+b_n)=$\_\_\_\_\_\_\_.

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