
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 $\dfrac{2\cos \left( \dfrac{3}{2}\pi+\theta\right)+\cos \left(\pi+\theta\right)}{3\sin (\pi-\theta)+2\sin \left( \dfrac{5}{2}\pi+\theta\right)}= \dfrac{1}{5}$;

$(1)$ Find the value of $\tan \theta$;

$(2)$ Find the value of ${\sin }^{2}\theta+3\sin \theta\cos \theta$.

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