
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 an arithmetic sequence $\{a_{n}\}$ with the formula for the sum of the first $n$ terms as $S_{n}$, $2a_{3}-a_{2}=5$, $S_{5}-S_{3}=14$.  
$(1)$ Find the general formula for $\{a_{n}\}$.  
$(2)$ If for all $n\in N^{*}$, $S_{n}-a_{n}+\lambda \geqslant 0$ always holds, find the range of values for $\lambda$.

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