
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 the sum of the first n terms of an arithmetic sequence ${a_n}$ is $S_n$, if $a_3 + a_4 = 7$, $S_5 = 15$, and the sum of the first n terms of the sequence ${\frac{1}{a_n a_{n+1}}}$ is $T_n$, then the value of $T_{10}$ is _______.

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