
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 $α \in \left(-\frac{π}{4},0\right)$ and $β \in \left(\frac{π}{2}, π\right)$, if $\cos(α+β) = -\frac{4}{5}$ and $\cos\left(β - \frac{π}{4}\right) = \frac{5}{13}$, find the value of $\cos\left(α + \frac{5π}{4}\right)$.

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