
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
In triangle $\triangle ABC$, $a=4$, $b=m$, $\sin A - \cos A = 0$. <br/> $(1)$ If $m=4\sqrt{2}$, then $c=$______; <br/> $(2)$ When $m=\_\_\_\_\_\_$ (write a possible value), there are two triangles $\triangle ABC$ that satisfy the condition.

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