
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 vectors $\overrightarrow {a}=(3,4), \overrightarrow {b}=(4,3), \overrightarrow {c}=\lambda \overrightarrow {a}- \overrightarrow {b} (\lambda\in\mathbb{R})$, and the angle between vector $\overrightarrow {c}$ and $\overrightarrow {a}$ is equal to the angle between $\overrightarrow {c}$ and $\overrightarrow {b}$, find the value of $\lambda$.

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