
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
In the Cartesian coordinate system, there are points $P_1$, $P_2$, ..., $P_n$, ... ($n\in\mathbb{N}^*$), with the coordinates of point $P_n$ being $(n, a_n)$, where $a_n = \frac{2}{n}$ ($n\in\mathbb{N}^*$). The line passing through points $P_n$ and $P_{n+1}$ forms a triangle with the coordinate axes, and the area of this triangle is denoted as $b_n$. Let $S_n$ represent the sum of the first $n$ terms of the sequence $\{b_n\}$. Find the value of $S_5$.

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