
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 the inequality about $x$, $\begin{vmatrix} x+m & 2 \\ 1 & x \end{vmatrix} < 0$, the solution set is $(-1,2)$.

(1) Find the value of the real number $m$;

(2) If $m\cos \alpha+2\sin \alpha=0$, find the value of $\tan (2\alpha- \frac{\pi}{4})$.

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