
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 the sequence $\left\{a_{n}\right\}$, define $\left\{ {\Delta _{1}}{a_{n}} \right\}$ as the first-order difference sequence of $\left\{a_{n}\right\}$, where ${\Delta _{1}}{a_{n}}={{a}_{{n+1}}}-{{a}_{n}}(n\in {\mathbb{N}^{*}})$. For a positive integer $k$, define $\left\{ {\Delta _{k}}{a_{n}} \right\}$ as the $k$-th order difference sequence of $\left\{a_{n}\right\}$, where ${\Delta _{k}}{a_{n}}={\Delta _{k-1}}{a_{n+1}}-{\Delta _{k-1}}{a_{n}}$. If the sequence $\left\{a_{n}\right\}$ satisfies ${a_{1}}=1$, ${{a}_{2}}=2$, and ${\Delta _{2}}{a_{n}}+{\Delta _{1}}{a_{n}}-{2}={0}(n\in {\mathbb{N}^{*}})$, find the value of ${{a}_{14}}$.

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