
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
Problem: Given the system of equations in terms of $x$ and $y$: $\left\{\begin{array}{l}{3x+7y=5m-3}\\{2x+3y=8}\end{array}\right.$, and the solution satisfies the equation $x+2y=5$, find the value of $m$. Students are discussing different solution methods:<br/>Student A says: We can first solve the system of equations in terms of $x$ and $y$: $\left\{\begin{array}{l}{3x+7y=5m-3}\\{2x+3y=8}\end{array}\right.$, and then find the value of $m$.<br/>Student B says: We can first add the two equations in the system $\left\{\begin{array}{l}{3x+7y=5m-3}\\{2x+3y=8}\end{array}\right.$, and then find the value of $m$.<br/>Student C says: We can first solve the system of equations $\left\{\begin{array}{l}{x+2y=5}\\{2x+3y=8}\end{array}\right.$, and then find the value of $m$.<br/>$\ldots $<br/>Please solve the above problem using $2$ different methods.

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