
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
Translate the following mathematical problem and its solution from Chinese to English, apply Markdown or Latex formatting, revise the solution to be step-by-step, and box the final answer.

Original problem and solution:
将函数\\(y=2\\sin (ωx- \\dfrac {π}{4})(ω > 0)\\)的图象分别向左、向右各平移\\( \\dfrac {π}{4}\\)个单位长度后，所得的两个图象对称轴重合，则\\(ω\\)的最小值为 \_\_\_\_\_\_ ．

解：把函数\\(y=2\\sin (ωx- \\dfrac {π}{4})(ω > 0)\\)的图象向左平移\\( \\dfrac {π}{4}\\)个单位长度后，所得图象对应的函数解析式为：
\\(y=2\\sin \[ω(x+ \\dfrac {π}{4})- \\dfrac {π}{4}\]=2\\sin (ωx+ \\dfrac {ω-1}{4}π)\\)，
向右平移\\( \\dfrac {π}{4}\\)个单位长度后，所得图象对应的函数解析式为：\\(y=2\\sin \[ω(x- \\dfrac {π}{4})- \\dfrac {π}{4}\]=2\\sin (ωx- \\dfrac {ω+1}{4}π).\\)
\\(∵\\)所得的两个图象对称轴重合，
\\(∴ωx+ \\dfrac {ω-1}{4}π=ωx- \\dfrac {ω+1}{4}π\\) \\(①\\)，或\\(ωx+ \\dfrac {ω-1}{4}π=ωx- \\dfrac {ω+1}{4}π+kπ\\)，\\(k∈Z\\)  \\(②\\)．
解\\(①\\)得\\(ω=0\\)，不合题意；
解\\(②\\)得\\(ω=2k\\)，\\(k∈Z\\)．
\\(∴ω\\)的最小值为\\(2\\)．
故答案为：\\(2\\)．
由三角函数的图象平移得到平移后的两个函数的解析式，再由两函数的对称轴重合得到\\(ωx+ \\dfrac {ω-1}{4}π=ωx- \\dfrac {ω+1}{4}π\\) 或\\(ωx+ \\dfrac {ω-1}{4}π=ωx- \\dfrac {ω+1}{4}π+kπ\\)，\\(k∈Z.\\)由此求得最小正数\\(ω\\)的值．
本题主要考查三角函数的平移，三角函数的平移原则为左加右减上加下减，考查了三角函数的对称性，是中档题．

Translated problem:
The graph of the function $y = 2 \sin\left(\omega x - \frac{\pi}{4}\right), \omega > 0$ is translated to the left and to the right by $\frac{\pi}{4}$ units, respectively. If the symmetry axes of the two resulting graphs overlap, find the smallest possible value of $\omega$.

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