
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 two arithmetic sequences \\(\left\{ a_n \right\}\\) and \\(\left\{ b_n \right\}\\), their sums of the first \\(n\\) terms are \\(S_n\\) and \\(T_n\\), respectively. If \\(\dfrac{S_n}{T_n} = \dfrac{2n+2}{n+3}\\), find the value of \\(\dfrac{a_{10}}{b_{10}}\\).

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