
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 $\{a_{n}\}$ with the first term ${a_1}=\frac{3}{5}$, and it satisfies ${a_{n+1}}=\frac{{3{a_n}}}{{2{a_n}+1}}$. If $\frac{1}{{{a_1}}}+\frac{1}{{{a_2}}}+…+\frac{1}{{{a_n}}}＜100$, then the maximum integer $n$ that satisfies the condition is $\_\_\_\_\_\_$.

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