
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 $a_1 + a_2 = 10$, $S_4 = 36$, find a direction vector of the line passing through points $P(n, a_n)$ and $Q(n+2, a_{n+2}) (n \in \mathbb{N}^*)$.

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