
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 $a \gt b \gt 0$ and $a+2b=3$.<br/>$(1)$ Find the range of values for $a$;<br/>$(2)$ Let $c=-3a+2b$, express $c$ in terms of $a$ algebraically, and find the range of values for $c$.

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