
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 a monotonically increasing arithmetic sequence $\{a_n\}$, the terms $a_3$, $a_7$, and $a_{15}$ form a geometric sequence, and the sum of the first five terms equals 20.

(1) Find the general formula for the sequence $\{a_n\}$;

(2) Let $b_n = \dfrac{2}{a_n a_{n+1}}$, and denote the sum of the first $n$ terms of the sequence $\{b_n\}$ as $T_n$. Find the maximum value of $n$ for which $T_n \leqslant \dfrac{24}{25}$ holds true.

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