
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 a sequence $\{a_n\}$ satisfying $a_{1}=1$ and $\left|a_{n}-a_{n-1}\right|= \frac {1}{2^{n}}$ for $n\geq2$ and $n\in\mathbb{N}$, and where $\{a_{2n-1}\}$ is a decreasing sequence and $\{a_{2n}\}$ is an increasing sequence, find the value of $5-6a_{10}$.

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