
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
Let  $n$  be a natural number. Find all solutions  $x$  of the system of equations   $$ \left\{\begin{matrix} sinx+cosx=\frac{\sqrt{n}}{2}tg\frac{x}{2}=\frac{\sqrt{n}-2}{3}\end{matrix}\right. $$   On interval  $\left[0,\frac{\pi}{4}\right).$ 

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