
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 a sequence $\{a_n\}$, where $a_1=1$, and the sum of the first $n$ terms is $S_n$, and point $P(a_n,a_{n+1})(n\in\mathbb{N}^*)$ lies on the line $x-y+1=0$, find the sum $\dfrac{1}{{S}_1}+ \dfrac{1}{{S}_2}+ \dfrac{1}{{S}_3}+\cdots+ \dfrac{1}{{S}_n}$.

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